Thermal printer and method of designing hot cathode fluorescent tube for thermal printer

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a thermal printer that achieves a reduction in print time.

2. Description of the Related Art

Conventionally, various means have been used in order to reduce the print time in color thermal printers that use thermal recording paper (referred to below as TA (Thermal-Autochrome) paper). One of these involves reducing the fixing time. Namely, in this type of printer, the ink fixing process is performed after the process to heat the thermal recording paper using the thermal head of the printer. This fixing process is carried out by light irradiated from a fluorescent lamp. The energy required to fix the ink is determined using the formula “light intensity”×“irradiation time”. Therefore, conventionally, various means have been employed to increase the intensity of the light using reflective plates.

However, conventionally, no means have been employed to strengthen the light emission intensity of the fluorescent lamp.

SUMMARY OF THE INVENTION

The present invention was conceived of in view of the above circumstances, and it is an object there of to provide thermal printer in which the light emission intensity of the fluorescent lamp is increased and, as a result, a reduction in the print time is achieved.

The present invention is intended to solve the above problems and the first aspect of the present invention is a thermal printer that performs color printing by carrying out a heating process via a thermal head on thermal recording paper provided with color forming layers for performing color formation in a plurality of different colors and by fixing the thermal recording paper that has undergone heating process using a light fixing device, wherein the light fixing device comprises: a hot cathode fluorescent lamp formed from: a fluorescent tube that has a fluorescent coating applied to an inside surface of the glass tube and inside which are sealed mercury and noble gases, filament electrodes provided at both ends of the fluorescent tube, and lead wires that supply power to the filament electrodes; and a magnetic circuit that is provided on a side surface of the fluorescent tube and that generates a magnetic field that acts on current that flows through the fluorescent tube when power is fed to the filament electrodes.

According to the present invention, in a thermal printer that performs color printing by carrying out a heating process on thermal recording paper using a thermal head and then fixing the thermal recording paper that has undergone the heat processing using light fixing device, because the light fixing device is formed from a hot cathode fluorescent lamp and a magnetic circuit that is provided on a side surface of the fluorescent tube and that generates a magnetic field that acts on the current flowing through the fluorescent tube when electricity is fed to the filament electrode, it is possible to increase the light emission intensity of the fluorescent lamp without shortening the life of the hot cathode fluorescent lamp. Moreover, the effective length of the fluorescent tube is improved by flattening the illumination intensity distribution by the illumination intensity in the vicinity of the filament electrodes being increased due to the magnetic circuit. As a result, the excellent effects are obtained that the print time is shortened, and uniform fixing can be made possible with unfixed areas or over fixed areas being done away with. Furthermore, because it is possible to maintain the maximum illumination intensity for a long period of time by providing a cooling fan for cooling the fluorescent tube, the excellent effect is obtained that the operating efficiency is vastly improved when the hot cathode fluorescent lamp is used for hardening resins that are hardened by ultraviolet light or for sterilization.

The second aspect of the present invention is the thermal printer according to the first aspect, wherein the magnetic circuit comprises a frame formed with a U shaped cross section from a ferromagnetic material, and a pair of magnets positioned such that different polarities face each end of the frame, and wherein the magnetic circuit is mounted on a side surface of the fluorescent tube so as to surround a lower half of the fluorescent tube.

The third aspect of the present invention is the thermal printer according to the second aspect, wherein a reflective plate is disposed between an end portion of the magnets and the fluorescent tube.

The fourth aspect of the present invention is the thermal printer according to the second aspect, wherein a surface of the magnets that faces the fluorescent tube is curved in a shape that substantially corresponds to a surface of the fluorescent tube, and that curved surface forms the reflective plate.

The fifth aspect of the present invention is the thermal printer according to the first aspect, wherein the magnetic circuit comprises a frame formed with a U shaped cross section from a ferromagnetic material, and a pair of magnets provided at both ends of the frame, and wherein a plurality of magnets are mounted in a row on a side surface of the fluorescent tube so as to surround a lower half of the fluorescent tube and so that polarities of adjacent magnets are different to each other.

The sixth aspect of the present invention is the thermal printer according to the first aspect, wherein the magnetic circuit comprises four magnets positioned at equal intervals along a peripheral surface of the fluorescent tube so that polarities of adjacent magnets are different to each other.

The seventh aspect of the present invention is the thermal printer according to the first aspect, wherein the magnetic circuit comprises a magnet shaped as a semicylinder, and more than half of an outer peripheral surface of the fluorescent tube is surrounded by a concave portion of the magnet.

The eighth aspect of the present invention is the thermal printer according to the first aspect, wherein the magnetic circuit comprises: a frame formed with a U shaped cross section from a ferromagnetic material and mounted so as to surround half a side surface of the hot cathode fluorescent lamp; and a pair of magnets positioned such that different polarities face each end of the frame and so as to sandwich one filament electrode of the hot cathode fluorescent lamp and a portion of the fluorescent tube.

The ninth aspect of the present invention is the thermal printer according to the first aspect, wherein the magnetic circuit comprises: a frame formed with a U shaped cross section from a ferromagnetic material and mounted so as to surround half a side surface of the hot cathode fluorescent lamp; and two pairs of magnets positioned such that different polarities face each end of the frame and so as to sandwich the filament electrodes at both ends of the hot cathode fluorescent lamp and a portion of the fluorescent tube.

The tenth aspect of the present invention is the thermal printer according to the eighth and ninth aspects, wherein a magnet used in the magnetic circuit is in a rectangular shape, a rectangular shape having one curved side, or a rectangular shape whose central portion has a different thickness to both end portions.

The eleventh aspect of the present invention is the thermal printer according to the first aspect, wherein the magnetic circuit comprises: a frame formed with a U shaped cross section from a ferromagnetic material and mounted so as to surround half a side surface of the hot cathode fluorescent lamp; and a pair of magnets mounted at both ends of the frame so as to sandwich the fluorescent tube; and two pairs of magnets positioned at both ends of the frame so as to sandwich the filament electrodes at both ends of the hot cathode fluorescent lamp and a portion of the fluorescent tube.

The twelfth aspect of the present invention is the thermal printer according to the eleventh aspect, wherein a magnet used in the magnetic circuit is in a rectangular shape, a rectangular shape having one side formed in a wave shape, or a rectangular shape whose thickness is formed in a wave shape.

The thirteenth aspect of the present invention is the thermal printer according to any one of the first to twelfth aspects, wherein a magnet used in the magnetic circuit is a ferrite magnet or a rare earth permanent magnet such as a samarium cobalt magnet.

The fourteenth aspect of the present invention is the thermal printer according to any of the first to twelfth aspects, wherein a magnet used in the magnetic circuit is an electromagnet formed from a soft porcelain material and a coil wound around the soft porcelain material.

The fifteenth aspect of the present invention is the thermal printer according to any of the first to fourteenth aspects, wherein the hot cathode fluorescent lamp is provided with a cooling fan at each end of the fluorescent tube for cooling the fluorescent tube.

The sixteenth aspect of the present invention is the thermal printer according to the fifteenth aspect, wherein the number of rotations of the cooling fan is controlled based on a surface temperature and illumination intensity of the fluorescent tube such that the illumination intensity is at maximum.

The seventeenth aspect of the present invention is a thermal printer comprising: moving device which moves thermal recording paper that is provided with color forming layers for performing color formation in a plurality of different colors in a first direction and in a second direction that is opposite to the first direction while the thermal recording paper is in a state of contact with a thermal head; first light fixing device provided at one side of the thermal head for fixing a first color; and second light fixing device provided at another side of the thermal head for fixing a second color, wherein the first and second fixing device comprise: a hot cathode fluorescent lamp formed from: a fluorescent tube that has a fluorescent coating applied to an inside surface of a glass tube and inside which are sealed mercury and noble gases, filament electrodes provided at both ends of the fluorescent tube, and lead wires that supply power to the filament electrodes; and a magnetic circuit that is provided on a side surface of the fluorescent tube and that generates a magnetic field that acts on current that flows through the fluorescent tube when power is fed to the filament electrodes.

According to the seventeenth aspect of the present invention, because there is no need to perform an operation to return the photosensitive material each time the printing of one color is completed, the effect is obtained that the time required to perform the printing operation can be shortened. In addition, according to the nineteenth aspect of the present invention, the effect is obtained that it is possible for the color formation of each color to be carried out at a predetermined position without there being any misalignment in the printing position.

The eighteenth aspect of the present invention is the thermal printer according to the seventeenth aspect, wherein the moving device is formed from a first pinch roller and a first feed roller provided at one adjacent side portion of the thermal head, a second pinch roller and a second feed roller provided at another adjacent side portion of the thermal head, and a pulse motor for driving the first and second feed rollers.

The nineteenth aspect of the present invention is the thermal printer according to the eighteenth aspect, the thermal printer further comprising: a first sensor provided in the vicinity of the first pinch roller and first feed roller for detecting a leading edge of the thermal recording paper; a second sensor provided in the vicinity of the second pinch roller and second feed roller for detecting a leading edge of the thermal recording paper; and printing start position determining device which supplies the pulse motor with a pulse number that is in accordance with a distance that a printing start position of the thermal recording paper is to be moved in order to be directly below the thermal head, based on results of detections by the first sensor and second sensor.

The twentieth aspect of the present invention is the thermal printer according to the thirteenth or nineteenth aspects, wherein there is provided a shutter for shutting off light from the first light fixing device at a point when fixing of the first color is completed.

The twenty first aspect of the present invention is a method of designing a hot cathode fluorescent tube that has a magnet and is structured such that a magnetic filed generated by the magnet acts on an electron flow so as to increase an illumination intensity, the method comprising: (a) a first step in which an empirical formula for representing a relationship between illumination intensity and magnetic energy density is derived from measurement values of illumination intensity and magnetic flux density inside the hot cathode fluorescent tube; (b) a second step in which initial values for a shape of the magnet are set; (c) a third step in which a model of the hot cathode fluorescent tube is created to be used for applying a finite element method; (d) a fourth step in which an evaluation coefficient that serves as an index for evaluating the shape of the magnet is derived using the empirical formula; and (e) a fifth step in which the finite element method is applied to the hot cathode fluorescent tube model and the shape of the magnet that was set to the initial values is optimized using the evaluation coefficient.

According to the twenty first aspect of the present invention, because the shape of the magnets is decided by numerical analysis, it is possible to optimize the magnet shape without having to rely on experience or intuition and the make the illumination intensity uniform over the entire effective length of the fluorescent tube.

The twenty second aspect of the present invention is the method of designing a hot cathode fluorescent tube according to the twenty first aspect, wherein, in the first step the magnetic flux density inside the hot cathode fluorescent tube and the illumination intensity when the magnet is mounted inside the hot cathode fluorescent tube are measured and the empirical formula is determined from the relationship between the illumination intensity and the magnetic flux density.

The twenty third aspect of the present invention is the method of designing a hot cathode fluorescent tube according to the twenty first or twenty second aspects, wherein, in the fourth step χ=(E

obj

/E

av

−1)

2

is used as the evaluation coefficient when E

obj

is taken as the illumination intensity when the magnet is not mounted and E

av

is taken as the average illumination intensity when the magnet is mounted.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1

is a schematic structural view showing the structure of the first embodiment of the present invention.

FIG. 2

is a cross sectional view showing the structure of the fixing lamp

7

in the first embodiment.

FIG. 3

is a view showing the operation of the fixing lamp

7

in FIG.

2

.

FIG. 4

is a graph showing an effect of the fixing lamp

7

shown in FIG.

2

.

FIGS. 5A and 5B

are views showing a system for measuring illumination intensity.

FIG. 6

is a cross sectional view showing the second embodiment of the present invention.

FIG. 7

is a cross sectional view showing the third embodiment of the present invention.

FIGS. 8A and 8B

are cross sectional views showing the fourth embodiment of the present invention.

FIGS. 9A and 9B

are cross sectional views showing the fifth embodiment of the present invention.

FIGS. 10A and 10B

are cross sectional views showing the sixth embodiment of the present invention.

FIG. 11

is a view of the structure when an electromagnet is used in

FIGS. 10A and 10B

.

FIGS. 12A and 12B

are cross sectional views showing the seventh embodiment of the present invention.

FIG. 13

is a cross sectional view showing the eleventh embodiment of the present invention.

FIG. 14

is a graph showing changes in the illumination intensity of the hot cathode fluorescent lamp according to the eleventh embodiment.

FIG. 15

is a cross sectional view showing the twelfth embodiment of the present invention.

FIG. 16

is a view showing the operation of the device when printing magenta color in the twelfth embodiment.

FIG. 17

is a block diagram showing the structure of an electrical circuit in the twelfth embodiment.

FIG. 18

is a schematic structural diagram showing the structure of the thermal printer in the thirteenth embodiment of the present invention.

FIG. 19

is a schematic structural diagram representing the state when the transporting direction is reversed in the thermal printer shown in FIG.

18

.

FIG. 20

is a graph showing the distribution of the illumination intensity of a conventional fixing lamp.

FIGS. 21A and 21B

are cross sectional views showing the eighth embodiment of the present invention.

FIG. 22

is a perspective view of a magnet.

FIGS. 23A and 23B

are perspective views of a magnet.

FIG. 24

is a graph for showing the effects of the fixing lamp

7

h.

FIGS. 25A and 25B

are cross sectional views showing the ninth embodiment of the present invention.

FIGS. 26A and 26B

are perspective views of a magnet.

FIG. 27

is a graph for showing the effects of the fixing lamp

7

i.

FIGS. 28A and 28B

are cross sectional views showing the tenth embodiment of the present invention.

FIGS. 29A and 29B

are perspective views of a magnet.

FIG. 30

is a graph for showing the effects of the fixing lamp

7

j.

FIG. 31

is a view showing the structure when an electromagnet is used.

FIG. 32

is a flow chart showing the optimized procedure of the fourteenth embodiment of the present invention.

FIGS. 33A and 33B

are views showing the values actually measured for the illumination intensity.

FIGS. 34A and 34B

are views showing the values actually measured for the magnetic flux density.

FIG. 35

is a view showing an example of a model of a fluorescent tube.

FIG. 36

is a view showing a split image of a fluorescent tube model.

FIG. 37

is a view used for describing the slice split positions of the fluorescent tube model.

FIG. 38

is a view showing the shape (widthwise) of an optimized magnet.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The embodiments of the present invention will now be described with reference made to the drawings.

FIG. 1

is a schematic structural view showing the structure of a thermal printer according to the first embodiment of the present invention. In the initial state before the printing operation is carried out, the thermal head

1

and pinch roller

4

are in a raised position separated respectively from a platen roller

2

and a feed roller

3

. In this state, if the power is turned on and the printing operation is started, TA paper

11

kept in the TA paper cassette

12

is fed toward a guide roller

6

by a feed out roller

5

.

Next, the TA paper

11

passes between the thermal head

1

and the platen roller

2

guided by the guide roller

6

and is transported to a point between the feed roller

3

and the pinch roller

4

. The thermal head

1

and the pinch roller

4

that had been lifted to raised positions are lowered, and the TA paper

11

is press contacted against the platen roller

2

and the feed roller

3

by the thermal head

1

and the pinch roller

4

. Next, the feed roller

3

rotates in a positive direction (i.e. in an anticlockwise direction) at a fixed speed and the thermal head

1

performs thermal color formation printing of the Y color (yellow).

When the leading portion of the Y color printing begins to appear at the left side of the feed roller

3

, the Y color fixing lamp

7

is turned on and light is irradiated onto the TA paper

11

. When the thermal color formation printing of the Y color is finished, the thermal head

1

is lifted up and, at the point when the rear end portion of the TA paper

11

arrives at the feed roller

3

, a shutter

13

is gradually moved towards the right, in a manner in which the light fixing amount remains constant, and ultimately covers the entire surface of the TA paper

11

. Next, when the Y color fixing lamp

7

is turned off, the shutter

13

is moved towards the left and is returned to its original position.

Next, the feed roller

3

is rotated in reverse (i.e. in a clockwise direction) and the TA paper

11

is fed in reverse until the leading portion of the TA paper

11

on which the printing has started arrives directly below the heat generating portion of the thermal head

1

. The M (magenta) color fixing lamp

9

and the Y color fixing lamp

7

are then slid together towards the top. At this time, the M (magenta) color fixing lamp

9

is slid to a predetermined position for irradiating light.

Next, the thermal head

1

is lowered downwards so as to place the TA paper

11

in press contact against the platen roller

2

and start the printing of the M color. At the same time as the printing of the M color is started the feed roller

3

is rotated in the positive direction and transports the TA paper

11

towards the left. When the leading portion on which the M color has been printed arrives at the left side of the feed roller

3

, the M color fixing lamp

9

is turned on and light is irradiated onto the TA paper

11

so as to perform the light fixing of the M color. Then, when the thermal color formation printing of the M color has ended, the thermal head

1

is lifted upwards.

Next, the feed roller

3

is rotated in reverse (i.e. in the clockwise direction) and the TA paper

11

is fed in reverse until the leading portion of the TA paper

11

on which the printing has started arrives directly below the heat generating portion of the thermal head

1

. The thermal head

1

is then lowered and the TA paper

11

is placed in press contact against the platen roller

2

so as to print the C (cyan) color. When the printing is completed, the TA paper

11

is ejected.

Next, the Y color fixing lamp

7

used in the above structure will be described.

FIG. 2

is a cross sectional view showing the structure of the fixing lamp

7

. This fixing lamp

7

is formed from a hot cathode fluorescent lamp. A fluorescent coating material is adhered to the entire inside surface of the glass tube of this lamp and a pair of electrodes are provided at both ends of the glass tube. Inside the tube are sealed noble gases such as argon gas and mercury. In this fixing lamp

7

, when filaments that are provided at both ends of the fluorescent tube

110

are heated by being energized from lead wires embedded in the caps, thermoelectrons are released from the filaments. The thermoelectrons collide with the mercury vapor vaporized inside the fluorescent tube and excite the mercury vapor. The excited mercury vapor releases energy in the form of ultraviolet light as it returns to a ground state. At this time, ultraviolet having a generated wavelength of 245 nm and 185 nm further excites the fluorescent material coated on the inside surface of the fluorescent tube and light in the ultraviolet and visible ranges, for example, light having a wavelength of 365 nm, 420 nm, and 450 nm is emitted.

Further, in

FIG. 2

, the symbol

103

denotes a frame formed with a U shaped cross section from a ferromagnetic material. The symbol

102

denotes a pair of magnets placed at both ends of the frame

103

and positioned such that the magnetic poles that face each other are different. A magnetic circuit is formed by the frame

103

and the pair of magnets

102

. Permanent magnets or electromagnets can be used as the magnets

102

. In the examples below the use of rare earth permanent magnets such as samarium cobalt magnets and the like is described. The magnetic circuit is mounted so as to surround the lower half of the side surface of the fluorescent tube

110

through the frame

103

.

FIG. 3

shows the magnetic flux distribution inside the fluorescent tube

110

. A description will now be given while referring to

FIG. 3

of the principle of increasing the illumination intensity of the fixing lamp

7

that is formed with the structure shown in FIG.

2

. High frequency voltage is applied to both ends of the fluorescent tube

110

shown in

FIG. 3

inside which mercury vapor has been sealed such that the polarities are cyclically changed. When the direction of the flow of the electric current

105

of the fluorescent tube

110

is towards this side at right angles to the surface of the drawing, the direction of the electron flow is in the opposite direction, namely, the flow is away from this side towards the far side. When the magnetic field

106

is acting at right angles to the current

105

, a force

107

acts on the current

105

(this is known as Fleming's left hand rule). This results in the electrons performing a magnetron operation that, compared with when the magnetic field

108

created by the permanent magnets is not present, has a markedly longer operation track and causes an increase in the acceleration distance and an increase in the chance of a collision with the mercury vapor. As a result, the light generating efficiency of the fixing lamp

7

is increased.

The changes over time in the illumination intensity when a hot cathode fluorescent lamp having the structure shown in

FIG. 2

is turned on and when a conventional hot cathode fluorescent lamp is turned are shown in FIG.

4

. The first curved line M

40

shows the changes in the illumination intensity of the fixing lamp

7

when 20 pairs of permanent magnets are mounted. The second curved line M

2

shows the changes in the illumination intensity of the fixing lamp

7

when one pair of permanent magnets is mounted. The third curved line M

0

shows the changes in the illumination intensity of a conventional hot cathode fluorescent tube. As is shown in

FIG. 7

, the peak illumination intensity increases as the number of permanent magnets used is increased and the magnetic flux intensity increased. It is thus possible to raise the illumination intensity by 50% or more compared with the illumination intensity of a conventional hot cathode fluorescent lamp. If the relationship between the number of permanent magnets used and the increase in the illumination intensity is looked at, it will be seen that the illumination intensity rises in proportion to the magnetic field intensity up to a certain point, however, after that point saturation occurs.

FIGS. 5A and 5B

show the measurement system used for measuring the above illumination intensity. The symbol

115

in

FIGS. 5A and 5B

indicates an illumination intensity sensor that is positioned at a distance of 15 mm from the fluorescent tube

110

. Samarium cobalt magnets are used for the permanent magnets

102

and these are mounted at both ends of a frame

103

made from zinc galvanized steel plate.

Next, a description will be given of the second embodiment of the present invention.

FIG. 6

is a cross sectional view showing the structure of the fixing lamp

7

a

according to the second embodiment of the present invention. In the fixing lamp

7

a

shown in this drawing, reflective plates

112

and

113

are formed in an integral structure between the end portion of the magnets

102

and the back portion of the fluorescent tube

110

(i.e. on the opposite side from the TA paper

11

). These reflective plates

112

and

113

are formed from aluminum or from a plastic film on the surface of which is coated by a vapor deposition method a reflective film formed from aluminum or the like. The symbol

114

indicates a permanent magnet that is attached to the frame

103

and that further intensifies the magnetic flux from the magnets

102

. Note that it is not necessary to provide the magnet

114

.

Next, a description will be given of the third embodiment of the present invention.

FIG. 7

is a cross sectional view showing the structure of the fixing lamp

7

b

according to the third embodiment of the present invention. In the fixing lamp

7

b

shown in this drawing, the shape of the magnet

102

in

FIG. 2

has been altered. Namely, one surface of each magnet

102

a

that faces the fluorescent tube

110

has been curved in a shape that corresponds substantially to the surface of the fluorescent tube

110

. This surface is smoothed and vapor deposited with aluminum to also fulfill the function of a reflective plate.

Next, a description will be given of the fourth embodiment of the present invention.

FIGS. 8A and 8B

show schematic cross sections of the fixing lamp

7

c

according to the fourth embodiment. As is shown in these drawings, a plurality of magnetic circuits are provided at equal intervals along the side surface of the fluorescent tube

110

. The plurality of magnetic circuits are positioned so that the polarities of adjacent magnets are different to each other.

FIG. 8A

shows an example of the provision of magnetic circuits. When the magnetic circuits are provided in this way, the magnetic flux is generated in the directions indicated by the arrows in the drawing and acts on the current flowing through the fluorescent tube

110

when the power is turned on thus increasing the illumination intensity.

Next, a description will be given of the fifth embodiment of the present invention.

FIGS. 9A and 9B

show schematic cross sections of the fixing lamp

7

d

according to the fifth embodiment. As is shown in these drawings, four magnets

125

a

to

125

d

are provided at equal intervals along the outer peripheral surface of the fluorescent tube

110

. The magnets

125

a

to

125

d

are positioned so that the polarities of adjacent magnets are different to each other. When the magnetic circuits are provided in this way, a magnetic field is generated in the directions indicated by the arrows and acts on the current flowing through the fluorescent tube

110

when the power is turned on thus increasing the illumination intensity.

Next, a description will be given of the sixth embodiment of the present invention.

FIGS. 10A and 10B

show schematic cross sections of the fixing lamp

7

e

according to the sixth embodiment. As is shown in these drawings, a semi cylindrical permanent magnet

131

is used for the magnetic circuit. The fluorescent tube

110

is mounted so that the concave portion of the semi cylindrical permanent magnet

131

surrounds more than half of the outer peripheral surface of the fluorescent tube

110

. When the magnetic circuit is provided in this way, a magnetic field is generated in the directions indicated by the arrows and acts on the current flowing through the fluorescent tube

110

thus increasing the illumination intensity.

Note that in the above described fixing lamp

7

e

, a permanent magnet is used, however, even when an electromagnet is used, it can be structured in the same way.

FIG. 11

is a view showing the structure when an electromagnet is used. The electromagnet is formed by winding a coil

136

around a soft porcelain material

135

and supplying electricity from a power source

137

.

Next, a description will be given of the seventh embodiment of the present invention.

FIGS. 12A and 12B

show schematic cross sections of the fixing lamp

7

f

according to the seventh embodiment. As is shown in the drawings, the feature of the present embodiment is that an electromagnet formed from an iron core

141

formed with a T shaped cross section and a coil

142

wound around the iron core

141

is mounted at the outer side of the fluorescent tube

110

. Electricity is supplied from a power source

143

to the coil

142

and magnetic flux is generated from the iron core

141

. By generating magnetic flux from the T shaped iron core

141

, it is possible for the magnetic field from a single electromagnet to act efficiently on the current flowing through the inside of the fluorescent tube

110

thus increasing the intensity of the illumination from the hot cathode fluorescent lamp.

Next, a description will be given of the eighth embodiment of the present invention. In the above described second to seventh embodiments, various modifications were made to the structure of the fixing lamp

7

of the first embodiment so as to intensify the illumination intensity of the fixing lamp

7

. In contrast, as is shown in

FIG. 20

, the distribution of the illumination intensity in the longitudinal direction of the fixing lamp

7

is not uniform and at both ends of the fluorescent tube

110

, i.e. at the portions marked A, the illumination intensity is reduced. In a hot cathode fluorescent tube used in a thermal printer, it is desirable if a uniform illumination intensity is obtained and if the effective length of the fluorescent tube that can actually be used is made as long as possible.

FIGS. 21A and 21B

show cross sections of the fixing lamp

7

h

according to the eighth embodiment. As is shown in these drawings, a magnetic circuit is formed from a frame

103

for mounting the magnets, and magnets

160

h

that are mounted such that the magnetic poles that face each other are different to each other. This magnetic circuit is provided in one filament electrode side of the fluorescent tube

110

.

FIG. 22

shows an example of a rectangular magnet having a maximum energy product of 33 MGOe used for the magnets

160

h.

FIG. 24

is a graph showing the effect when the magnet shown in

FIG. 22

is used. The curved line NT in

FIG. 24

shows the illumination intensity distribution when the magnets

160

h

are not mounted, while the curved line Mh shows the illumination intensity distribution when the magnets

160

h

are mounted. It is possible to improve the effective length by mounting the magnets

160

h.

In order to improve the effective length even further, magnets having the shapes shown in

FIGS. 23A and 23B

are used. The magnet shown in

FIG. 23A

has a constant thickness and a shape in which one side of the rectangle is convexly curved so that the illumination intensity distribution is made flat. In contrast, the magnet shown in

FIG. 23B

has a rectangular shape and the thickness of both ends thereof are decreased in comparison with the center part so as to achieve a flattening of the illumination intensity distribution.

Next, a description will be given of the ninth embodiment of the present invention.

FIGS. 25A and 25B

show cross sections of the fixing lamp

7

i

according to the ninth embodiment. As is shown in these drawings, two magnetic circuits are formed from a frame

103

, and two pairs of magnets

160

i

that are mounted such that the magnetic poles thereof that face each other are different to each other. The two magnetic circuits are arranged so that one is provided in the filament electrode side at each end of the fluorescent tube

110

.

FIG. 27

is a graph showing the effect when rectangular magnets are used as the magnets

160

i

. The curved line NT in

FIG. 27

shows the illumination intensity distribution when the magnets

160

i

are not mounted, while the curved line Mi shows the illumination intensity distribution when the magnets

160

i

are mounted. The effective length is improved by mounting the magnets

160

i.

As is shown by the illumination intensity distribution Mi, it is possible to improve the effective length through the use of the rectangular magnets

160

i

, however, because a peak is created in the illumination intensity distribution, in order to improve the effective length and flatness even more, magnets having the shapes shown in

FIGS. 26A

or

26

B are used. The magnet shown in

FIG. 26A

is shaped with one side of the magnet curved to become gradually narrower so that the illumination intensity in the vicinity of the filament electrodes is strengthened, the increase in the illumination intensity is adjusted by gradually weakening the magnetic force, and the flatness of the illumination intensity distribution is improved. Moreover, the magnet shown in

FIG. 26B

achieves flatness in the illumination intensity distribution and adjusts the increase in the illumination intensity by changing the magnetic force by altering the thickness of the magnet to form a wedge shape.

Next, a description will be given of the tenth embodiment of the present invention.

FIGS. 28A and 28B

show cross sections of the fixing lamp

7

j

according to the tenth embodiment. As is shown in these drawings, magnetic circuits are formed from a frame

103

as well as a pair of magnets

160

j

and two pairs of magnets

161

j

that are mounted such that the facing magnetic poles thereof are different to each other. The magnets

160

j

are long enough to act on the entire fluorescent tube

110

and increase the illumination intensity of the entire hot cathode fluorescent lamp. The two magnetic circuits formed using the magnets

161

j

are arranged so that one is provided in the filament electrode side at each end of the fluorescent tube

110

so as to raise the illumination intensity in the vicinity of the filament electrodes and achieve flatness in the illumination intensity distribution.

FIG. 30

is a graph showing the effect when rectangular magnets are used for the magnets

160

j

and

161

j

. The curved line NT in

FIG. 30

shows the illumination intensity distribution when the magnets

160

j

and

161

j

are not mounted, while the curved line Mh shows the illumination intensity distribution when the magnets

160

j

and

161

j

are mounted. It is possible to improve the illumination intensity and effective length by mounting the magnets

160

j

and

161

j

. In order to achieve even more uniformity in the illumination intensity distribution, magnets having the shapes shown in

FIGS. 29A and 29B

are used for the magnets

161

j

. The magnet shown in

FIG. 29A

has a shape in which one side is formed in a wave shape so that the width of the magnet is made to vary thereby adjusting the magnetic force and achieving a flattening in the illumination intensity distribution by changing the degree to which the illumination intensity is increased. In the magnet shown in

FIG. 29B

the thickness is changed in a wave shape so as to adjust the magnetic force and achieve a flattening in the illumination intensity.

FIG. 31

shows an example of when the above described magnets

160

h

to

160

j

and

161

j

are formed from electromagnets

165

.

Next, a description will be given of the eleventh embodiment of the present invention.

FIG. 13

shows the structure of the fixing lamp

7

g

according to the eleventh embodiment. As is shown in

FIG. 13

, a cooling fan

151

is mounted at each end of the fluorescent tube

110

. As a result of the surface of the fluorescent tube

110

being cooled by the cooling fans

151

, an intensified illumination intensity is able to be maintained for a long period of time. The rotation of the cooling fan

151

is controlled, based on values measured for the illumination intensity of the fixing lamp

7

g

and the surface temperature of the fluorescent tube, such that the illumination intensity is at the maximum.

FIG. 14

is a graph showing the changes in the illumination intensity over time when a conventional hot cathode fluorescent lamp is turned on and when the fixing lamp having the structure shown in

FIG. 13

is turned on. The first curved line MA shows the changes in the illumination intensity when the fixing lamp

7

in which a magnetic circuit is provided (see

FIG. 1

) is cooled using the cooling fans

151

provided at each end thereof.

The second curved line MB shows the changes in the illumination intensity when the fixing lamp

7

in which an magnetic circuit is provided is not cooled, while the third curved line NT shows the changes in the illumination intensity when a conventional hot cathode fluorescent lamp with no cooling is used. As is shown by the curved lines MB and NT, when the fluorescent tube

110

is not cooled, the illumination intensity decreases over time from the peak illumination intensity. In contrast, the curved line MA shows that it is possible to maintain the peak illumination intensity over a long period of time by cooling the fluorescent tube

110

using the cooling fans

151

.

Next, a description will be given of the twelfth and thirteenth embodiments of the present invention. In the above described second to eleventh embodiments various modifications were made to the structure fixing lamp according to the first embodiment, however, in the embodiments described below, modifications are made to the rest of the structure apart from the fixing lamp

7

.

FIG. 15

is a block diagram showing the twelfth embodiment of the present invention.

FIG. 17

is a block diagram showing the connections of a control section

50

. In these diagrams the symbol

20

indicates TA paper comprising a substrate such as paper or synthetic paper on which has been coated a color forming agent and a developer. The symbol

21

indicates a thermal head having a heat generating portion on the surface thereof that contacts the platen roller

22

. The thermal head then sandwiches the TA paper between the heat generating portion and a platen roller

22

and the heat generating portion performs a heating process on the TA paper

20

so as to perform thermal color development on the TA paper

20

. The operation of this heating process by the thermal head

21

is based on control signals output from the control section

50

and the operation to print the TA paper

20

is carried out in the direction in which the TA paper

20

is transported.

A feed roller

23

and a pinch roller

24

sandwich the TA paper

20

, and the feed roller

23

is rotated when it receives rotation force transmitted from a pulley

31

so as to transport the TA paper

20

. The symbol

25

indicates a Y (yellow) color fixing lamp for irradiating light for fixing Y color on the TA paper

20

. A fixing lamp having the same structure as one of the fixing lamps

7

and

7

a

to

7

g

of the above described first to eighth embodiments is used for the fixing lamp

25

. The symbol

26

indicates a reflective plate for raising the light irradiation efficiency by reflecting light irradiated from the Y color fixing lamp

25

onto the TA paper

20

.

A feed roller

27

and a pinch roller

28

sandwich the TA paper

20

, and the feed roller

27

is rotated when it receives rotation force transmitted from a pulley

33

so as to transport the TA paper

20

. The symbol

29

indicates an M (magenta) color fixing lamp for fixing M color on the TA paper

20

after the printing of the M color has been carried out. A fixing lamp having the same structure as one of the fixing lamps

7

and

7

a

to

7

g

of the above described first to eighth embodiments is used for the fixing lamp

29

. The symbol

30

indicates a reflective plate for raising the light irradiation efficiency by reflecting light irradiated from the M color fixing lamp

29

onto the TA paper

20

.

A pulse motor

32

rotates at a constant angle of rotation each time in accordance with the number of pulses output from the control section

50

. A pulley

39

is fixed to the rotation shaft of this pulse motor

32

and the pulley

39

is linked to the pulley

31

and the pulley

33

via a belt

34

. As a result, the feed roller

23

and the feed roller

27

can be driven to rotate.

A sensor

45

is formed from a light emitting diode and a light receiving diode. The light receiving diode receives light irradiated from the light emitting diode. When the TA paper

20

passes between the pinch roller

24

and the feed roller

23

, the light irradiated from the light emitting diode to the light receiving diode is cut off. Consequently, it is possible to detect that the TA paper

20

has arrived between the pinch roller

24

and the feed roller

23

. The result of this detection is then output to the control section

50

.

In the same way, a sensor

46

formed from a light emitting diode and a light receiving diode is provided between the pinch roller

28

and the feed roller

27

. The sensor

46

detects that the TA paper

20

has arrived between the pinch roller

28

and the feed roller

27

and outputs the detection result to the control section

50

.

Next, the control section

50

will be described. As is shown in

FIG. 17

, the control section

50

is connected to each section and performs the control of the raising and lowering operations of the pinch roller

24

and the pinch roller

28

, the heating process of the thermal head

21

, the rotation operation of the pulse motor

32

based on detection signals output from the sensor

45

and the sensor

46

, the turning on and off of the Y color fixing lamp

25

and the M color fixing lamp

29

, the opening and closing operations of the shutter

40

, and the like (described in detail below).

Next, a description will be given of the device having the above described structure. Firstly, in

FIG. 15

, the thermal head

21

is in contact with the platen roller

22

and the pinch roller

24

is in contact with the feed roller

23

, however, in the initial state before printing is started, the thermal head

21

and the pinch roller

24

are lifted up and separated from the platen roller

22

and the feed roller

23

respectively.

In this state, when printing is begun, the TA paper

20

is transported in the direction indicated by the arrow from the left hand side in

FIG. 15

by a paper supply roller and passes between the feed roller

27

and the pinch roller

28

and between the thermal head

21

and the platen roller

22

. Next, when the portion of the TA paper that is at the front in the direction of travel (referred to below as the distal end portion) arrives between the feed roller

23

and the pinch roller

24

, the fact that the TA paper

20

has arrived is detected by the sensor

45

and a detection signal is output to the control section

50

.

When the control section

50

receives the detection signal from the sensor

45

, the pinch roller

24

is lowered downwards and placed in press contact with the feed roller

23

thus nipping the TA paper

20

. In addition, the thermal head

21

is also lowered downwards and placed in press contact with the platen roller

22

thus nipping the TA paper

20

.

The control section

50

then outputs to the pulse motor

32

a pulse number that accords with the distance to travel from the distal end portion of the TA paper

20

to the printing start position. The pulse motor

32

rotates in accordance with the output pulse number thereby rotating the feed roller

32

via the belt

34

and pulley

31

. The printing start position of the TA paper

20

is thus transported to a position directly below the thermal head

21

.

Next, the control section

50

performs the control of the heating process operation for the Y (yellow) color in accordance with the image being printed. Subsequently, the control section

50

rotates the pulse motor

32

so as to rotate the feed roller

23

and thereby perform the printing operation while the TA paper

20

is being transported in the direction indicated by the arrow.

Next, after the control section

50

has output to the pulse motor

32

pulses in accordance with the distance the printed distal; end portion is to travel between the feed roller

23

and the pinch roller

24

, the control section

50

turns on the Y color fixing lamp

25

and fixes the Y color on the TA paper

20

. As a result, color formation of the Y color does not occur thereafter on the TA paper

20

even if heat is applied from the thermal head

21

.

After the Y color printing operation has been completed, when the end portion on which the Y color has been printed is transported to the right side of the feed roller

23

, the control section

50

stops the rotation of the pulse motor

32

. The shutter

40

is then moved to the left at a uniform speed and covers the surface of the TA paper shutting off the light irradiated from the Y color fixing lamp

25

so that the Y color fixing amount on the surface of the TA paper

20

is made constant.

Next, after the shutter

40

has covered the front surface of the TA paper

20

, the control section

50

turns off the Y color fixing lamp

25

and moves the shutter

40

to a predetermined position at the right. Subsequently, the thermal head

21

is lifted up and the thermal head

21

and the platen roller

22

are separated. Next, the feed roller

23

is rotated in an anticlockwise direction so that the rear end portion of the TA paper

20

is transported in the direction indicated by the arrow in FIG.

16

.

When the TA paper

20

is transported such that the distal end portion of the TA paper

20

is detected by the sensor

46

, the control section

50

lowers the pinch roller

28

placing it in press contact with the feed roller

27

. The thermal head

21

is also lowered placing it in press contact with the platen roller

22

. In addition, the pinch roller

24

is lifted up, separating the pinch roller

24

from the feed roller

23

. By then rotating the feed roller

27

, the TA paper

20

is transported in the direction indicated by the arrow in FIG.

16

.

The control section

50

then outputs to the pulse motor

32

a pulse number that accords with the distance to travel from the distal end portion of the TA paper

20

to the printing start position for the M (magenta) color. The pulse motor

32

rotates in accordance with the output pulse number thereby rotating the feed roller

27

via the belt

34

and pulley

33

. The M color printing start position of the TA paper

20

is thus transported to a position directly below the thermal head

21

.

Next, the control section

50

performs the control of the heating process operation for the M color in accordance with the image being printed. Subsequently, the control section

50

rotates the pulse motor

32

so as to rotate the feed roller

27

and thereby perform the printing operation while the TA paper

20

is being transported in the direction indicated by the arrow. As a result, the printing of the M color is performed on the TA paper

20

.

Next, after the control section

50

has output to the pulse motor

32

pulses in accordance with the distance the printed distal end portion is to travel between the feed roller

27

and the pinch roller

28

, the control section

50

turns on the M color fixing lamp

29

and fixes the M color on the TA paper

20

. As a result, color formation of the M color does not occur thereafter on the TA paper

20

even if heat is applied from the thermal head

21

.

After the M color printing operation has been completed, when the end portion on which the M color has been printed is transported to the left side of the feed roller

27

, the control section

50

stops the rotation of the pulse motor

32

in accordance with a predetermined time required for the fixing of the M color. Thereafter the M color fixing lamp

29

is turned off, the thermal head

21

is lifted up and the thermal head

21

and the platen roller

22

are separated. Next, the feed roller

27

is rotated in a clockwise direction so that the rear end portion of the TA paper

20

is transported in the direction indicated by the arrow in FIG.

15

.

When the TA paper

20

is transported such that the distal end portion of the TA paper

20

is detected by the sensor

45

, the control section

50

lowers the pinch roller

24

placing it in press contact with the feed roller

23

. The thermal head

21

is also lowered placing it in press contact with the platen roller

22

. In addition, the pinch roller

28

is lifted up, separating the pinch roller

28

from the feed roller

27

. By then rotating the feed roller

23

, the TA paper

20

is transported in the direction indicated by the arrow in FIG.

15

.

The control section

50

then outputs to the pulse motor

32

a pulse number that accords with the distance to travel from the distal end portion of the TA paper

20

to the printing start position for the C (cyan) color. The pulse motor

32

rotates in accordance with the output pulse number thereby rotating the feed roller

23

via the belt

34

and pulley

31

. The C color printing start position of the TA paper

20

is thus transported to a position directly below the thermal head

21

.

Next, the control section

50

performs the control of the heating process operation for the C color in accordance with the image being printed. Subsequently, the control section

50

rotates the pulse motor

32

so as to rotate the feed roller

27

and thereby perform the C color printing operation while the TA paper

20

is being transported in the direction indicated by the arrow. As a result, the printing of the C color is performed on the TA paper

20

. After the printing of the C color has been completed, the control section

50

discharges the TA paper

20

via the paper discharge roller thus completing the printing process.

Next, a description will be given of the thirteenth embodiment of the present invention using

FIGS. 18 and 19

. In

FIGS. 18 and 19

, the transmission means for the power output from the pulse motor

32

in

FIG. 15

, namely, the belt

34

, the pulley

31

, and the pulley

39

have been replaced with an idle gear

37

, a clutch

35

, and a clutch

36

. In

FIG. 18

, the rotation shaft of the pulse motor

32

is linked to the idle gear

37

via a gear

38

, and the clutch

35

and the clutch

36

are also linked to the idle gear

37

. The clutch

35

is engaged with the feed roller

23

and when the clutch

36

is disengaged, the TA paper is transported in the direction indicated by the arrow in

FIG. 18

(i.e. towards the right) by the rotation of the pulse motor

32

.

In contrast,

FIG. 19

shows the state when the clutch

35

is disengaged and the clutch

36

is engaged with the feed roller

27

. In this case, the TA paper is transported in the direction indicated by the arrow in

FIG. 19

(i.e. towards the left) by the rotation of the pulse motor

32

. In this embodiment, the operations to engage and disengage the clutch

35

and the clutch

36

are controlled by the control section

50

. Moreover, in

FIGS. 18 and 19

, because the rotation force is transmitted by the engaging and disengaging of the clutches

35

and

36

, the pinch roller

24

and the pinch roller

28

are placed in constant press contact with the feed roller

23

and the feed roller

27

. Because the remainder of the printing operation is the same as in the twelfth embodiment, a description thereof is omitted.

Next, a description will be given of the fourteenth embodiment of the present invention using

FIGS. 32 through 37

.

In the above embodiments, the shape of the magnets and the mounting positions were determined experimentally by experience and intuition so as to obtain a uniform illumination intensity distribution. In the fourteenth embodiment, a method is described that enables the shape of the magnets of the hot cathode fluorescent tube to be optimized by calculation, that enables the illumination intensity to be increased and made more uniform, and that enables the uniform illumination intensity range to be expanded without having to rely on experience and intuition.

Firstly, an outline of the procedure for calculating the shape of the magnets using numerical analysis according to the finite element method will be described.

In

FIG. 32

the procedure for calculating the shape of a magnet using the finite element method is shown. In step S

1

shown in this diagram, the magnetic flux density of an area corresponding to the inside of a fluorescent tube is measured using a plurality of magnets having different magnetic force. From the values measured, an empirical formula is derived that represents the relationship between the illumination intensity and the magnetic energy density. Furthermore, using this empirical formula, an evaluation function that forms an index for evaluating the magnet shape is derived. In step S

2

, the initial shape of the magnet (i.e. the initial value for the shape) in the numerical analysis is determined. In step S

3

, a model of a fluorescent tube to be used for applying the finite element method is created.

In step S

4

, the magnet shape is optimized by applying the finite element method to the model of a fluorescent tube created in step S

3

. Namely, optimization calculation is performed according to the finite element method by changing the magnet shape with the shape of the magnet determined in step S

2

as the initial value while evaluating the magnet shapes using the aforementioned evaluation function (step S

4

A). Next, a determination is made as to whether or not the results of the optimization calculation converge (step S

4

B). If the calculation results do not converge (i.e. if the determination in step S

4

B is NO), the optimization calculation is repeated. If the calculation results do converge (i.e. if the determination in step S

4

B is YES), the shape of the magnet is set from the calculation results at that time (step S

4

C).

The contents of the above described procedure will now be described in detail.

A. Empirical Formula Representing the Relationship Between the Magnetic Energy and the Illumination Intensity

An empirical formula representing the relationship between the illumination intensity and the magnetic energy density is derived on the basis of data obtained by measuring the relationship between the illumination intensity and magnetic flux density. Here, the relationship between the two is derived due to it being considered that as, a result of the magnetic energy being converted into kinetic energy of the mercury vapor, the number of times it collides with the fluorescent coating is increased thereby raising the illumination intensity.

(a) Measuring the Illumination Intensity

The illumination intensity distribution of the fluorescent tube is determined by actual measurement.

FIG. 33A

shows the positional relationships between an illumination intensity meter

200

, a fluorescent tube

201

, and a magnet

203

at the time the illumination intensity distribution was measured. In this example, the effective length (i.e. the length apart from the cap portions) of the fluorescent tube

201

is 280 mm. The distance d

1

from the surface of the magnet

203

to the surface of the fluorescent tube

201

is 6 mm for a magnet with low magnetic force and 6.7 mm for a magnet with high magnetic force. The distance between the illumination intensity meter

200

and the fluorescent tube

201

is 8 mm.

FIG. 33B

is a graph showing an example of values measured for the illumination intensity distribution of the fluorescent tube

201

. The horizontal axis in

FIG. 33B

is the distance from the left side of the effective length of the fluorescent tube

201

minus the cap portion, while the vertical axis is the illumination intensity at positions specified by the distance on the horizontal axis. The curved line EL

1

in the graph represents the illumination intensity distribution when no magnet is mounted, the curved line EL

2

represents the illumination intensity distribution when the magnet with low magnetic force is mounted, while the curved line EL

3

represents the illumination intensity when the magnet with high magnetic force is mounted. As can be understood from this graph, when the shape of the magnets has not been optimized, the illumination intensities in the vicinities of the end portions of the fluorescent tube are greatly reduced and the illumination intensity is not uniform.

(b) Measuring the Magnetic Flux Density

The magnetic flux density inside the fluorescent tube

201

is determined by actual measurement.

FIG. 34A

shows the points A to G where the magnetic flux of the magnet

203

was measured. Taking the center axis of the fluorescent tube

201

as the point of origin (the point C), the measurement points were set on two circumferences that had radiuses r of 4 mm and 8 mm respectively.

FIG. 34B

shows the values measured for the magnetic flux density at the measurement points A to G and shows an instance of the values measured when the magnet with high magnetic force was used as the magnet

203

and of the values measured when the magnet with low magnetic force was used as the magnet

203

. In this way, the magnetic flux density was measured at the respective measurement points using a plurality of magnets each having different magnetic force.

(c) Derivation of the Relational Expression Between the Magnetic Energy Density and the Illumination Intensity

The magnetic energy density is calculated from the above described values measured for the magnetic flux density, and the relationship between the magnetic energy density and the illumination intensity determined.

Firstly, the magnetic flux density B at an arbitrary point on the system of coordinates shown in

FIG. 34A

is approximated using Formula (1) below.

B=a·r+b ·θ+c·r·θ+d

(1)

Wherein a, b, c, and d are coefficients, r is a variable representing the distance from the point of origin (the point C) in the circumferential system of coordinates, and θ is a variable representing the angle of rotation on the circumferential system of coordinates.

Looking next at the point at which the magnetic energy U is proportional to the inner product of vectors of the magnetic flux density B (i.e. B·B), for the areas R

1

to R

4

shown in

FIG. 34A

, the magnetic energy density w is determined by setting the coefficients a to d of Formula (1) and integrating B

2

using the variables r and θ, and then by totaling the integral values of each area and dividing by the total area. In the example shown in

FIG. 34B

, when the magnet having a high magnetic force is used, a magnetic energy density of 9.179×10

−4

was obtained. When the magnet having a low magnetic force was used, a magnetic energy density of 3.347×10

−4

was obtained.

Next, the relationship between the magnetic energy density w and the illumination intensity E was approximated using the quadratic formula shown in Formula (2).

E=a

1

w

2

+b

1

w+c

1

(2)

Wherein a

1

, b

1

, and c

1

are coefficients.

If the value of the illumination intensity and the magnetic energy density w calculated from the aforementioned magnetic energy U are substituted in formula (2) and apposed, the coefficients a

1

, b

1

, and c

1

are determined. In the present embodiment, the coefficients a

1

, b

1

, and c

1

are calculated from the relationship between the illumination and the magnetic energy density obtained for positions from the end of the fluorescent tube of 100 mm, 150 mm, and 200 mm. Among these, the coefficients a

1

=−8.17×10

4

, b

1

=6.61×10

2

, and c

1

=2.19 that were obtained for the position at 150 mm, which had the least divergence in the illumination intensity, were employed. The derivation process for these coefficients is described below.

2. Magnet Shape Optimization Calculation Using the Finite Element Method

(a) Formation of a Fluorescent Tube Model

A model of a fluorescent tube used for the application of the finite element method was created.

FIG. 35

shows an example of a model of a fluorescent tube. In

FIG. 35

the symbol

204

indicates a frame formed from a ferromagnetic material and having a U shaped cross section. In the present embodiment, the width W

1

of the frame

204

was set at 22.5 mm, the length thereof was set at 280 mm, the height H

1

of one side wall was set at 10.25 mm, the height of the other side wall H

2

was set at 15 mm, and the thickness (no descriptive symbol) of the frame

204

was set at 1 mm. The frame

204

was positioned so as to cover a portion of the fluorescent tube

201

.

The symbol

203

indicates a magnet (having a width W

2

and a height H

3

) disposed on the frame

204

so as to face the fluorescent tube

201

and extending in the longitudinal direction of the fluorescent tube

201

. A magnetic circuit is formed by the magnet

203

and the frame

204

. In the present embodiment, the width W

2

of the magnet

203

is changed and the shape of the magnet

203

is changed so that illumination intensity distribution of the semicircular fluorescent area having the height H

4

shown in

FIG. 35

is made constant. In the present embodiment, the height H

4

is set at 7.75 mm.

FIG. 36

shows a split image of a fluorescent tube model. The numerical analysis performed using the finite element method is carried out for each element set in these split positions. In the example shown in

FIG. 37

, the split positions P

1

to P

4

and P

6

to P

9

are set at 20 mm intervals. In addition, the interval between the split position P

4

and P

5

is set to 80 mm, while the interval between the split position P

5

and P

6

is set to 60 mm. As is shown in this diagram, the intervals of the splits in the vicinity of the caps of the fluorescent tube are set at a small size. By making slice splits in this way, the numerical analysis at both ends where the illumination intensity distribution changes can be performed with a high level of accuracy.

(b) Evaluation Coefficient

The evaluation coefficient χ used when optimizing the shape of the magnet. In the present embodiment, Formula (3) below is employed as χ such that the value when the shape of the magnet has been optimized is at 0.

χ=

E

obj

/E

av

−1)

2

(3)

Wherein E

obj

indicates the illumination intensity obtained by substituting the average illumination intensity at each slice position when no magnet is mounted in the above Formula (2) for the coefficient C

1

. E

av

indicates the average illumination intensity at each slice position when a magnet is mounted in the above Formula (2).

(c) Optimization Calculation (Numerical Analysis Using the Finite Element Method)

When the illumination intensity E obj is equal to the average illumination intensity E av and the shape of the magnet has been optimized according to the evaluation coefficient χ shown in Formula (3), the coefficient value is close to zero. In the present embodiment, the width W

2

of the magnet is used as the design variable representing the shape of the magnet, and the width W

2

of the magnet is optimized at each slice split position using the finite element method such that the evaluation coefficient χ becomes close to zero. In the present embodiment, the initial value of the width W

2

of the magnet is set to 1 mm, and this width W

2

of the magnet is varied between 1 and 13 mm so as to determine the optimum magnet width.

(d) Results of the Numerical Analysis Using the Finite Element Method

In

FIG. 38

the width W

2

of the magnet at each slice split position obtained as a result of the optimization calculation is shown. As is shown in this drawing, the width W

2

of the magnet is large in the vicinity of the cap where the illumination intensity is low when no magnet has been mounted. Moreover, the width W

2

of the magnet remains at the initial value of 1 mm in the vicinity of the center where the illumination intensity distribution is high. In this way, according to the fourteenth embodiment, without relying on experience or intuition, the width W

2

of the magnet is set by numerical analysis so as to compensate for the reduction in the illumination intensity and an illumination intensity distribution that is uniform and at a high level can be obtained over the entire longitudinal direction of the fluorescent tube.

Next, a detailed description will be given for reference of the derivation process for the coefficients of the empirical formula shown in Formula (2) above.

Firstly, using the measurement values shown in

FIG. 34B

, each coefficient of a formula representing the magnetic flux density B on the circumferential system of coordinates shown in Formula (1) above is determined.

In the area R

1

shown in

FIG. 34A

, the x component and the y component of the magnetic flux density B are looked at separately.

Formula (10A) representing the x components of the magnetic flux density B (B

1

x

to B

4

x

) in the area R

1

is obtained from the measurement values when the magnet shown in

FIG. 34B

that has a large magnetic force is used. Formula (10B) is obtained by re-expressing the x components of the magnetic density flux (B

1

x

to B

4

x

) after substituting r and θ representing the measurement points on the circumferential system of coordinates in Formula (1). Formula (10C) is obtained from the formulas (10A) and (10B). Formula (10C) gives the coefficients (ax, bx, cx, and dx) of the x components of the magnetic flux density B in the area R

1

as the coefficients (a, b, c, and d) in Formula (1). In the same way, the formulas (10D) and (10E) representing the y components of the magnetic flux density B (B

1

y

to B

4

y

) in the area R

1

are obtained. Formula (10F) is obtained from the formulas (10D) and (10E). Formula (10F) gives the coefficients (ay, by, cy, and dy) of the y components of the magnetic flux density B in the area R

1

as the coefficients (a, b, c, and d) in Formula (1).

\begin{matrix} [\begin{matrix} \begin{matrix} \begin{matrix} B1x \\ B2x \end{matrix} \\ B3x \end{matrix} \\ B4x \end{matrix}] = [\begin{matrix} \begin{matrix} \begin{matrix} 0 \\ 0 \end{matrix} \\ 0.0245 \end{matrix} \\ 0.0356 \end{matrix}] & (10A) \\ [\begin{matrix} \begin{matrix} \begin{matrix} B1x \\ B2x \end{matrix} \\ B3x \end{matrix} \\ B4x \end{matrix}] = [\begin{matrix} 4 \cdot 10^{- 3} & 0 & 0 & 1 \\ 8 \cdot 10^{- 3} & 0 & 0 & 1 \\ 4 \cdot 10^{- 3} & \frac{π}{2} & 2 \cdot π \cdot 10^{- 3} & 1 \\ 8 \cdot 10^{- 3} & \frac{π}{2} & 4 \cdot π \cdot 10^{- 3} & 1 \end{matrix}] \cdot [\begin{matrix} \begin{matrix} \begin{matrix} ax \\ bx \end{matrix} \\ cx \end{matrix} \\ dx \end{matrix}] & (10B) \\ [\begin{matrix} \begin{matrix} \begin{matrix} ax \\ bx \end{matrix} \\ cx \end{matrix} \\ dx \end{matrix}] = [\begin{matrix} \begin{matrix} \begin{matrix} 0 \\ 8.531 \cdot 10^{- 3} \end{matrix} \\ 1.767 \end{matrix} \\ 0 \end{matrix}] & (10C) \\ [\begin{matrix} \begin{matrix} \begin{matrix} B1y \\ B2y \end{matrix} \\ B3y \end{matrix} \\ B4y \end{matrix}] = [\begin{matrix} \begin{matrix} \begin{matrix} 0.022 \\ 0.013 \end{matrix} \\ 0.03 \end{matrix} \\ 0.015 \end{matrix}] & (10D) \\ [\begin{matrix} \begin{matrix} \begin{matrix} B1y \\ B2y \end{matrix} \\ B3y \end{matrix} \\ B4y \end{matrix}] = [\begin{matrix} 4 \cdot 10^{- 3} & 0 & 0 & 1 \\ 8 \cdot 10^{- 3} & 0 & 0 & 1 \\ 4 \cdot 10^{- 3} & \frac{π}{2} & 2 \cdot π \cdot 10^{- 3} & 1 \\ 8 \cdot 10^{- 3} & \frac{π}{2} & 4 \cdot π \cdot 10^{- 3} & 1 \end{matrix}] \cdot [\begin{matrix} \begin{matrix} \begin{matrix} ay \\ by \end{matrix} \\ cy \end{matrix} \\ dy \end{matrix}] & (10E) \\ [\begin{matrix} \begin{matrix} \begin{matrix} ay \\ by \end{matrix} \\ cy \end{matrix} \\ dy \end{matrix}] = [\begin{matrix} \begin{matrix} \begin{matrix} - 2.25 \\ 8.913 \cdot 10^{- 3} \end{matrix} \\ - 0.955 \end{matrix} \\ 0.031 \end{matrix}] & (10F) \end{matrix}

In the same way, the coefficients (a

2

x

to d

2

x

) of the x components of the magnetic flux density B and the coefficients (a

2

y

to d

2

y

) of the y components of the magnetic flux density B are determined in Formula (1) for the area R

2

. These calculation processes are shown in the formulas (11A) to (11F).

\begin{matrix} [\begin{matrix} \begin{matrix} \begin{matrix} B1x \\ B2x \end{matrix} \\ B3x \end{matrix} \\ B4x \end{matrix}] = [\begin{matrix} \begin{matrix} \begin{matrix} 0 \\ 0 \end{matrix} \\ 0 \end{matrix} \\ 0.0245 \end{matrix}] & (11A) \\ [\begin{matrix} \begin{matrix} \begin{matrix} B1x \\ B2x \end{matrix} \\ B3x \end{matrix} \\ B4x \end{matrix}] = [\begin{matrix} 0 & 0 & 0 & 1 \\ 4 \cdot 10^{- 3} & 0 & 0 & 1 \\ 0 & \frac{π}{2} & 0 & 1 \\ 4 \cdot 10^{- 3} & \frac{π}{2} & 2 \cdot π \cdot 10^{- 3} & 1 \end{matrix}] [\begin{matrix} \begin{matrix} \begin{matrix} a2x \\ b2x \end{matrix} \\ c2x \end{matrix} \\ d2x \end{matrix}] & (11B) \\ [\begin{matrix} \begin{matrix} \begin{matrix} a2x \\ b2x \end{matrix} \\ c2x \end{matrix} \\ d2x \end{matrix}] = [\begin{matrix} \begin{matrix} \begin{matrix} 0 \\ 0 \end{matrix} \\ 3.899 \end{matrix} \\ 0 \end{matrix}] & (11C) \\ [\begin{matrix} \begin{matrix} \begin{matrix} B1y \\ B2y \end{matrix} \\ B3y \end{matrix} \\ B4y \end{matrix}] = [\begin{matrix} \begin{matrix} \begin{matrix} 0.038 \\ 0.022 \end{matrix} \\ 0.038 \end{matrix} \\ 0.03 \end{matrix}] & (11D) \\ [\begin{matrix} \begin{matrix} \begin{matrix} B1y \\ B2y \end{matrix} \\ B3y \end{matrix} \\ B4y \end{matrix}] = [\begin{matrix} 0 & 0 & 0 & 1 \\ 4 \cdot 10^{- 3} & 0 & 0 & 1 \\ 0 & \frac{π}{2} & 0 & 1 \\ 4 \cdot 10^{- 3} & \frac{π}{2} & 2 \cdot π \cdot 10^{- 3} & 1 \end{matrix}] \cdot [\begin{matrix} \begin{matrix} \begin{matrix} a2y \\ b2y \end{matrix} \\ c2y \end{matrix} \\ d2y \end{matrix}] & (11E) \\ [\begin{matrix} \begin{matrix} \begin{matrix} a2y \\ b2y \end{matrix} \\ c2y \end{matrix} \\ d2y \end{matrix}] = [\begin{matrix} \begin{matrix} \begin{matrix} - 4 \\ 0 \end{matrix} \\ 1.273 \end{matrix} \\ 0.038 \end{matrix}] & (11F) \end{matrix}

In the same way, the coefficients (a

3

x

to d

3

x

) of the x components of the magnetic flux density B and the coefficients (a

3

y

to d

3

y

) of the y components of the magnetic flux density B are determined in Formula (1) for the area R

3

. These calculation processes are shown in the formulas (12A) to (12F).

\begin{matrix} [\begin{matrix} \begin{matrix} \begin{matrix} B1x \\ B2x \end{matrix} \\ B3x \end{matrix} \\ B4x \end{matrix}] = [\begin{matrix} \begin{matrix} \begin{matrix} 0.0245 \\ 0.0356 \end{matrix} \\ 0.0 \end{matrix} \\ 0.0 \end{matrix}] & (12A) \\ [\begin{matrix} \begin{matrix} \begin{matrix} B1x \\ B2x \end{matrix} \\ B3x \end{matrix} \\ B4x \end{matrix}] = [\begin{matrix} 4 \cdot 10^{- 3} & \frac{π}{2} & 2 \cdot π \cdot 10^{- 3} & 1 \\ 8 \cdot 10^{- 3} & \frac{π}{2} & 4 \cdot π \cdot 10^{- 3} & 1 \\ 4 \cdot 10^{- 3} & π & 4 \cdot π \cdot 10^{- 3} & 1 \\ 8 \cdot 10^{- 3} & π & 8 \cdot π \cdot 10^{- 3} & 1 \end{matrix}] \cdot [\begin{matrix} \begin{matrix} \begin{matrix} a3x \\ b3x \end{matrix} \\ c3x \end{matrix} \\ d3x \end{matrix}] & (12B) \\ [\begin{matrix} \begin{matrix} \begin{matrix} a3x \\ b3x \end{matrix} \\ c3x \end{matrix} \\ d3x \end{matrix}] = [\begin{matrix} \begin{matrix} \begin{matrix} 5.55 \\ - 8.531 \cdot 10^{- 3} \end{matrix} \\ - 1.767 \end{matrix} \\ 0.027 \end{matrix}] & (12C) \\ [\begin{matrix} \begin{matrix} \begin{matrix} B1y \\ B2y \end{matrix} \\ B3y \end{matrix} \\ B4y \end{matrix}] = [\begin{matrix} \begin{matrix} \begin{matrix} 0.03 \\ 0.015 \end{matrix} \\ 0.05 \end{matrix} \\ 0.01 \end{matrix}] & (12D) \\ [\begin{matrix} \begin{matrix} \begin{matrix} B1y \\ B2y \end{matrix} \\ B3y \end{matrix} \\ B4y \end{matrix}] = [\begin{matrix} 4 \cdot 10^{- 3} & 0 & 0 & 1 \\ 8 \cdot 10^{- 3} & 0 & 0 & 1 \\ 4 \cdot 10^{- 3} & \frac{π}{2} & 2 \cdot π \cdot 10^{- 3} & 1 \\ 8 \cdot 10^{- 3} & \frac{π}{2} & 4 \cdot π \cdot 10^{- 3} & 1 \end{matrix}] \cdot [\begin{matrix} \begin{matrix} \begin{matrix} a3y \\ b3y \end{matrix} \\ c3y \end{matrix} \\ d3y \end{matrix}] & (12E) \\ [\begin{matrix} \begin{matrix} \begin{matrix} a3y \\ b3y \end{matrix} \\ c3y \end{matrix} \\ d3y \end{matrix}] = [\begin{matrix} \begin{matrix} \begin{matrix} 2.5 \\ 0.029 \end{matrix} \\ - 3.979 \end{matrix} \\ 0 \end{matrix}] & (12F) \end{matrix}

In the same way, the coefficients (a

4

x

to d

4

x

) of the x components of the magnetic flux density B and the coefficients (a

4

y

to d

4

y

) of the y components of the magnetic flux density B are determined in Formula (1) for the area R

4

. These calculation processes are shown in the formulas (13A) to (13F).

\begin{matrix} [\begin{matrix} \begin{matrix} \begin{matrix} B1x \\ B2x \end{matrix} \\ B3x \end{matrix} \\ B4x \end{matrix}] = [\begin{matrix} \begin{matrix} \begin{matrix} 0 \\ 0.0245 \end{matrix} \\ 0.0 \end{matrix} \\ 0.0 \end{matrix}] & (13A) \\ [\begin{matrix} \begin{matrix} \begin{matrix} B1x \\ B2x \end{matrix} \\ B3x \end{matrix} \\ B4x \end{matrix}] = [\begin{matrix} 0 & \frac{π}{2} & 0 & 1 \\ 4 \cdot 10^{- 3} & \frac{π}{2} & 2 \cdot π \cdot 10^{- 3} & 1 \\ 0 & π & 0 & 1 \\ 4 \cdot 10^{- 3} & π & 4 \cdot π \cdot 10^{- 3} & 1 \end{matrix}] \cdot [\begin{matrix} \begin{matrix} \begin{matrix} a4x \\ b4x \end{matrix} \\ c4x \end{matrix} \\ d4x \end{matrix}] & (13B) \\ [\begin{matrix} \begin{matrix} \begin{matrix} a4x \\ b4x \end{matrix} \\ c4x \end{matrix} \\ d4x \end{matrix}] = [\begin{matrix} \begin{matrix} \begin{matrix} 12.25 \\ 0 \end{matrix} \\ - 3.899 \end{matrix} \\ 0 \end{matrix}] & (13C) \\ [\begin{matrix} \begin{matrix} \begin{matrix} B1y \\ B2y \end{matrix} \\ B3y \end{matrix} \\ B4y \end{matrix}] = [\begin{matrix} \begin{matrix} \begin{matrix} 0.038 \\ 0.03 \end{matrix} \\ 0.038 \end{matrix} \\ 0.05 \end{matrix}] & (13D) \\ [\begin{matrix} \begin{matrix} \begin{matrix} B1y \\ B2y \end{matrix} \\ B3y \end{matrix} \\ B4y \end{matrix}] = [\begin{matrix} 0 & \frac{π}{2} & 0 & 1 \\ 4 \cdot 10^{- 3} & \frac{π}{2} & 2 \cdot π \cdot 10^{- 3} & 1 \\ 0 & π & 0 & 1 \\ 4 \cdot 10^{- 3} & π & 4 \cdot π \cdot 10^{- 3} & 1 \end{matrix}] \cdot [\begin{matrix} \begin{matrix} \begin{matrix} a4y \\ b4y \end{matrix} \\ c4y \end{matrix} \\ d4y \end{matrix}] & (13E) \\ [\begin{matrix} \begin{matrix} \begin{matrix} a4y \\ b4y \end{matrix} \\ c4y \end{matrix} \\ d4y \end{matrix}] = [\begin{matrix} \begin{matrix} \begin{matrix} - 7 \\ 0 \end{matrix} \\ 3.183 \end{matrix} \\ 0.038 \end{matrix}] & (13F) \end{matrix}

Next, the coefficients (a

5

x

to d

5

x

), (a

6

x

to d

6

x

), (a

7

x

to d

7

x

), and (a

8

x

to d

8

x

) that give the x components in the magnetic flux density B and the coefficients (a

5

y

to d

5

y

), (a

6

y

to d

6

y

), (a

7

y

to d

7

y

), and (a

8

y

to d

8

y

) that give the y components in the magnetic flux density B in Formula (1) are determined for the areas R

1

to R

4

in the same way from the measurement values when the magnet shown in

FIG. 34B

that has a small magnetic force is used. These calculation results are shown in Formulas (14) to (17).

\begin{matrix} [\begin{matrix} \begin{matrix} \begin{matrix} a5x \\ b5x \end{matrix} \\ c5x \end{matrix} \\ d5x \end{matrix}] = [\begin{matrix} \begin{matrix} \begin{matrix} 0 \\ 9.167 \cdot 10^{- 3} \end{matrix} \\ - 0.35 \end{matrix} \\ 0 \end{matrix}], [\begin{matrix} \begin{matrix} \begin{matrix} a5y \\ b5y \end{matrix} \\ c5y \end{matrix} \\ d5y \end{matrix}] = [\begin{matrix} \begin{matrix} \begin{matrix} 0.625 \\ 7.958 \cdot 10^{- 3} \end{matrix} \\ - 1.114 \end{matrix} \\ 2 \cdot 10^{- 3} \end{matrix}] & (14) \\ [\begin{matrix} \begin{matrix} \begin{matrix} a6x \\ b6x \end{matrix} \\ c6x \end{matrix} \\ d6x \end{matrix}] = [\begin{matrix} \begin{matrix} \begin{matrix} 0 \\ 0 \end{matrix} \\ 1.942 \end{matrix} \\ 0 \end{matrix}], [\begin{matrix} \begin{matrix} \begin{matrix} a6y \\ b6y \end{matrix} \\ c6y \end{matrix} \\ d6y \end{matrix}] = [\begin{matrix} \begin{matrix} \begin{matrix} 1.625 \\ - 3.82 \cdot 10^{- 3} \end{matrix} \\ 0.875 \end{matrix} \\ 7 \cdot 10^{- 3} \end{matrix}] & (15) \\ [\begin{matrix} \begin{matrix} \begin{matrix} a7x \\ b7x \end{matrix} \\ c7x \end{matrix} \\ d7x \end{matrix}] = [\begin{matrix} \begin{matrix} \begin{matrix} - 1.1 \\ - 9.167 \cdot 10^{- 3} \end{matrix} \\ 0.35 \end{matrix} \\ 0.029 \end{matrix}], [\begin{matrix} \begin{matrix} \begin{matrix} a7y \\ b7y \end{matrix} \\ c7y \end{matrix} \\ d7y \end{matrix}] = [\begin{matrix} \begin{matrix} \begin{matrix} - 10 \\ - 0.015 \end{matrix} \\ 5.65 \end{matrix} \\ 0.039 \end{matrix}] & (16) \\ [\begin{matrix} \begin{matrix} \begin{matrix} a8x \\ b8x \end{matrix} \\ c8x \end{matrix} \\ d8x \end{matrix}] = [\begin{matrix} \begin{matrix} \begin{matrix} 6.1 \\ 0 \end{matrix} \\ - 1.942 \end{matrix} \\ 0 \end{matrix}], [\begin{matrix} \begin{matrix} \begin{matrix} a8y \\ b8y \end{matrix} \\ c8y \end{matrix} \\ d8y \end{matrix}] = [\begin{matrix} \begin{matrix} \begin{matrix} - 2.475 \\ 0 \end{matrix} \\ 1.448 \end{matrix} \\ 0.013 \end{matrix}] & (17) \end{matrix}

As a result of the above, each coefficient of Formula (1) representing the magnetic flux density B in the circumferential system of coordinates is obtained for when a magnet having a large magnetic force is used and for when a magnet having a small magnetic force is used.

Next, the magnetic energy density is determined using Formula (1).

Generally, the magnetic energy density w, is represented by the following Formula (18).

\begin{matrix} wi = \frac{1}{2 S} \int \int_{S} H \cdot B ⅆ s = \frac{1}{2 μ S} \int \int_{S} B \cdot B ⅆ s & (18) \end{matrix}

Wherein S is the surface area (in the present embodiment, S is the surface area of the areas R

1

to R

4

). Moreover, μ is the magnetic permeability.

The details of the calculation formula for the integration portion in Formula (18) when the magnet having a large magnetic force shown in

FIG. 34B

is used are shown in Formulas (20A) to (20D) for the areas R

1

to R

4

. In these formulas, bb

1

to bb

4

represents the respective calculation results of the integration portion for the areas R

1

to R

4

. In this embodiment, bb

1

=2.655×10

−8

, bb

2

=1.27×10

−8

, bb

3

=3.755×10

−8

, and bb

4

=2.091×10

−8

are obtained. The magnetic energy density w when the magnet having a large magnetic force is used is represented by Formula (20E) and is obtained by totaling the calculation results of Formulas (20A) to (20D) and dividing this by the surface area of the areas R

1

to R

4

. In the present embodiment, 9.719×10

−4

is obtained as the magnetic energy density w.

\begin{matrix} bb1 = \int_{4 \cdot 10^{- 3}}^{8 \cdot 10^{- 3}} \int_{0}^{\frac{π}{2}} [{(ax \cdot r + bx \cdot θ + cx \cdot r \cdot θ + dx)}^{2} + {(ay \cdot r + by \cdot θ + cy \cdot r \cdot θ + dy)}^{2}] \cdot r ⅆ θ ⅆ r & (20A) \\ bb2 = \int_{0}^{4 \cdot 10^{- 3}} \int_{0}^{\frac{π}{2}} [{(a2x \cdot r + b2x \cdot θ + c2x \cdot r \cdot θ + d2x)}^{2} + {(a2y \cdot r + b2y \cdot θ + c2y \cdot r \cdot θ + d2y)}^{2}] \cdot r ⅆ θ ⅆ r & (20B) \\ bb3 = \int_{4 \cdot 10^{- 3}}^{8 \cdot 10^{- 3}} \int_{\frac{π}{2}}^{π} [{(a3x \cdot r + b3x \cdot θ + c3x \cdot r \cdot θ + d3x)}^{2} + {(a3y \cdot r + b3y \cdot θ + c3y \cdot r \cdot θ + d3y)}^{2}] \cdot r ⅆ θ ⅆ r & (20C) \\ bb4 = \int_{0}^{4 \cdot 10^{- 3}} \int_{\frac{π}{2}}^{π} [{(a4x \cdot r + b4x \cdot θ + c4x \cdot r \cdot θ + d4x)}^{2} + {(a4y \cdot r + b4y \cdot θ + c4y \cdot r \cdot θ + d4y)}^{2}] \cdot r ⅆ θ ⅆ r & (20D) \\ w = \frac{(bb1 + bb2 + bb3 + bb4)}{\frac{{(8 \cdot 10^{- 3})}^{2} \cdot π}{2}} & (20E) \end{matrix}

In the same way, the details of the calculation formula for the integration portion in Formula (18) when the magnet having a small magnetic force shown in

FIG. 34B

is used are shown in Formulas (21A) to (21D) for the areas R

1

to R

4

. In these formulas, bb

5

to bb

8

represents the respective calculation results of the integration portion for the areas R

1

to R

4

. in this embodiment, bb

5

=3.232×10

−9

, bb

6

=1.678×10

−9

, bb

7

=2.535×10

−8

, and bb

8

=3.384×10

−9

are obtained. The magnetic energy density w

2

when the magnet having a small magnetic force is used is represented by Formula (21E) and is obtained by totaling the calculation results of Formulas (21A) to (21D) and dividing this by the surface area of the areas R

1

to R

4

. In the present embodiment, 3.347×10

−4

is obtained as the magnetic energy density w

2

.

\begin{matrix} bb5 = \int_{4 \cdot 10^{- 3}}^{8 \cdot 10^{- 3}} \int_{0}^{\frac{π}{2}} [{(a5x \cdot r + b5x \cdot θ + c5x \cdot r \cdot θ + d5x)}^{2} + {(a5y \cdot r + b5y \cdot θ + c5y \cdot r \cdot θ + d5y)}^{2}] \cdot r ⅆ θ ⅆ r & (21A) \\ bb6 = \int_{0}^{4 \cdot 10^{- 3}} \int_{0}^{\frac{π}{2}} [{(a6x \cdot r + b6x \cdot θ + c6x \cdot r \cdot θ + d6x)}^{2} + {(a6y \cdot r + b6y \cdot θ + c6y \cdot r \cdot θ + d6y)}^{2}] \cdot r ⅆ θ ⅆ r & (21B) \\ bb7 = \int_{4 \cdot 10^{- 3}}^{8 \cdot 10^{- 3}} \int_{\frac{π}{2}}^{π} [{(a7x \cdot r + b7x \cdot θ + c7x \cdot r \cdot θ + d7x)}^{2} + {(a7y \cdot r + b7y \cdot θ + c7y \cdot r \cdot θ + d7y)}^{2}] \cdot r ⅆ θ ⅆ r & (21C) \\ bb8 = \int_{0}^{4 \cdot 10^{- 3}} \int_{\frac{π}{2}}^{π} [{(a8x \cdot r + b8x \cdot θ + c8x \cdot r \cdot θ + d8x)}^{2} + {(a8y \cdot r + b8y \cdot θ + c8y \cdot r \cdot θ + d8y)}^{2}] \cdot r ⅆ θ ⅆ r & (21D) \\ w2 = \frac{(bb5 + bb6 + bb7 + bb8)}{\frac{{(8 \cdot 10^{- 3})}^{2} \cdot π}{2}} & (21E) \end{matrix}

The magnetic energy density was thus obtained in the manner described above.

Next, the coefficients of Formula (2) that represent the relationship between the illumination intensity and the magnetic energy density are determined.

Formula (22) below is obtained by re-expressing Formula (2) using the magnetic energy density when the magnet having a large magnetic force is used and the magnetic energy density when the magnet having a small magnetic force is used.

\begin{matrix} \begin{matrix} E1 = a \cdot w^{2} + b \cdot w + c \\ E2 = a \cdot {w2}^{2} + b \cdot w2 + c \end{matrix}} & (22) \end{matrix}

Formula (23A) is obtained from the measurement values of the illumination intensity when the position from the end of the fluorescent tube is 200 mm. Moreover, when Formula (22) is re-expressed as a matrix formula, Formula (23B) is obtained. Formula (23C) is obtained from the formulas (23A) and (23B). The coefficients (a, b, and c) given by Formula (23C) give the coefficients of Formula (2) when the position from the end of the fluorescent tube is 200 mm.

\begin{matrix} [\begin{matrix} \begin{matrix} E1 \\ E2 \end{matrix} \\ E0 \end{matrix}] = [\begin{matrix} \begin{matrix} 2.672 \\ 2.345 \end{matrix} \\ 2.196 \end{matrix}] & (23A) \\ [\begin{matrix} \begin{matrix} E1 \\ E2 \end{matrix} \\ E0 \end{matrix}] = [\begin{matrix} w^{2} & w & 1 \\ {w2}^{2} & w2 & 1 \\ 0 & 0 & 1 \end{matrix}] \cdot [\begin{matrix} \begin{matrix} a \\ b \end{matrix} \\ c \end{matrix}] & (23B) \\ [\begin{matrix} \begin{matrix} a \\ b \end{matrix} \\ c \end{matrix}] = [\begin{matrix} \begin{matrix} 6.999 \cdot 10^{4} \\ 421.75 \end{matrix} \\ 2.196 \end{matrix}] & (23C) \end{matrix}

In the same way, Formula (24A) is obtained from the measurement values of the illumination intensity when the position from the end of the fluorescent tube is 150 mm. Moreover, when Formula (22) is re-expressed in this case as a matrix formula, Formula (24B) is obtained. Formula (24C) is obtained from Formula (24A) and Formula (24B). The coefficients (a

1

, b

1

, and c

1

) given by Formula (24C) give the coefficients of Formula (2) when the position from the end of the fluorescent tube is 150 mm.

As described above, in the present embodiment, the coefficients (a

1

, b

1

, and c

1

) when the position is 150 mm from the end of the fluorescent tube is used for the reason that there is little divergence in the illumination intensity.

\begin{matrix} [\begin{matrix} \begin{matrix} E11 \\ E21 \end{matrix} \\ E01 \end{matrix}] = [\begin{matrix} \begin{matrix} 2.757 \\ 2.404 \end{matrix} \\ 2.192 \end{matrix}] & (24A) \\ [\begin{matrix} \begin{matrix} E1 \\ E2 \end{matrix} \\ E0 \end{matrix}] = [\begin{matrix} w^{2} & w & 1 \\ {w2}^{2} & w2 & 1 \\ 0 & 0 & 1 \end{matrix}] \cdot [\begin{matrix} \begin{matrix} a1 \\ b1 \end{matrix} \\ c1 \end{matrix}] & (24B) \\ [\begin{matrix} \begin{matrix} a1 \\ b1 \end{matrix} \\ c1 \end{matrix}] = [\begin{matrix} \begin{matrix} - 8.17 \cdot 10^{4} \\ 660.749 \end{matrix} \\ 2.192 \end{matrix}] & (24C) \end{matrix}

In the same way, Formula (25A) is obtained from the measurement values of the illumination intensity when the position from the end of the fluorescent tube is 100 mm. When Formula (22) is re-expressed in this case as a matrix formula, Formula (25B) is obtained. Formula (25C) is obtained from Formula (25A) and Formula (25B). The coefficients (a

2

, b

2

, and c

2

) given by Formula (25C) give the coefficients of Formula (2) when the position from the end of the fluorescent tube is 100 mm.

\begin{matrix} [\begin{matrix} \begin{matrix} E12 \\ E22 \end{matrix} \\ E02 \end{matrix}] = [\begin{matrix} \begin{matrix} 2.744 \\ 2.38 \end{matrix} \\ 2.167 \end{matrix}] & (25A) \\ [\begin{matrix} \begin{matrix} E1 \\ E2 \end{matrix} \\ E0 \end{matrix}] = [\begin{matrix} w^{2} & w & 1 \\ {w2}^{2} & w2 & 1 \\ 0 & 0 & 1 \end{matrix}] \cdot [\begin{matrix} \begin{matrix} a2 \\ b2 \end{matrix} \\ c2 \end{matrix}] & (25B) \\ [\begin{matrix} \begin{matrix} a2 \\ b2 \end{matrix} \\ c2 \end{matrix}] = [\begin{matrix} \begin{matrix} - 6.701 \cdot 10^{4} \\ 658.82 \end{matrix} \\ 2.167 \end{matrix}] & (25C) \end{matrix}

Number	Date	Country
12-245363	Aug 2000	JP
12-402276	Dec 2000	JP
13-203981	Jul 2001	JP

Number	Name	Date	Kind
4417172	Touhou et al.	Nov 1983	A
4692661	Moskowitz et al.	Sep 1987	A
4698547	Grossman et al.	Oct 1987	A
4833488	Mizutani et al.	May 1989	A
5825396	Fujishiro	Oct 1998	A

Thermal printer and method of designing hot cathode fluorescent tube for thermal printer

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