Patent Grant
8736199
The microwave electron gun, first described in U.S. Pat. No. 4,641,103, has proven to be a highly effective source of electrons for applications requiring high peak current and high beam quality such as free electron lasers and accelerators for particle physics research. Broadly, such a gun subjects the electrons emitted from a cathode to an intense microwave electric field for acceleration, and then typically blocks all but a narrow range of momentum to provide the bunching required by the linear accelerator. The gun comprises a resonant microwave cavity and a cathode mounted in the cavity wall.
The resonant microwave cavity, when supplied with microwave power, supports an electromagnetic field having a high-gradient electric component directed along an acceleration axis. The cavity is formed with an exit aperture at a location relative to the cathode such that emitted electrons are accelerated along the axis and pass through the exit aperture. Bunching, if required, is provided by a momentum analyzer system, which may include a dispersive magnet and a slit. An electron emerging from the cavity has an energy (energy and momentum have a one-to-one relationship, and thus will sometimes be used interchangeably) determined by the phase of the microwave field at the time of that electron's emission. The magnet causes electrons with different energies to follow different trajectories, while the slit is disposed to block those electrons having energies outside a desired narrow range of energies and phases. Thus, only those electrons having energies corresponding to a narrow range of phases are permitted to pass through the momentum analyzer, thereby forming a pre-bunched electron beam for injection into a linear accelerator.
However, use of the technology has been complicated by the back-heating phenomenon, in which electrons emitted from the cathode late in the accelerating phase of the applied microwave field are decelerated by the field before they escape the cavity, and are returned to the cathode with sufficient energy to raise the cathode temperature (and hence the emitted current density) as time progresses during the pulse. While the phenomenon has little impact on operation for modest emitted currents and short RF pulses, the temperature rise for higher cathode currents and/or longer pulses can substantially alter the beam current during the pulse, causing the energy of the electrons leaving the cavity to droop due to beam loading. In the worst case, this can lead to thermal runaway in which the cathode temperature rises uncontrollably due to ever-increasing back-heating. These electrons are referred to as backstreaming electrons.
Efforts to eliminate back-heating have included application of a transverse magnetic field to deflect the backstreaming electrons so that they strike the walls of the cavity surrounding the cathode instead of the cathode, and optimization of the dimensions and configuration of the cavity to reduce the chances that the electrons emitted late in the accelerating phase of the field will be returned to the cathode. An attempt has also been made to use ring-shaped or toroidal cathodes to exploit the tendency of the back-heating electrons in these designs to return to the cathode near the axis where they would strike a non-emissive component of the cathode assembly. None of these approaches has succeeded in reducing the temperature rise of the cathode to the level in which cathode emission remains substantially constant during the pulse.
In embodiments of the present invention, the temperature rise due to the backstreaming electrons is canceled by an equal and opposite fall in temperature at the surface of the cathode due to the conduction of heat deposited at the surface immediately prior to the microwave pulse by a pulsed laser focused to uniformly illuminate the cathode surface. Variations in temperature across the surface of the cathode attributable to the non-uniform spatial distribution of the backstreaming electrons may be compensated using a second laser pulse fired during the RF pulse to maintain constant thermal power input across the surface of the cathode during the RF pulse. This second pulse can also be used to compensate for the time-dependent rate of decay of temperature due to conduction of the heat deposited by the first laser into the body of the cathode.
Although U.S. Pat. No. 4,641,103 included a description of the use of a pulsed ultraviolet laser to enhance or control emission from the cathode of a microwave gun, or to reduce the cathode temperature required for operation of the gun, the laser described in U.S. Pat. No. 4,641,103 served to increase electron emission, not to reduce the temperature of the cathode during emission. And while the literature also includes a description of a microwave gun in which a laser is used to heat the cathode, that application describes the use of a continuous laser applied to the rear surface of the cathode and therefore intrinsically unable to achieve the temperature control described in this invention.
Accordingly, the invention described herein is novel, and can substantially improve the operation of the microwave electron guns described in the prior art.
A representative embodiment of the invention includes:
As a possible alternative embodiment of the invention, the spatial profile of the second illuminating laser can be modified to achieve cathode current spatial profiles matched to specific applications by controlling the spatial profile of the cathode surface temperature.
As a second possible embodiment of the invention, the second pulsed illuminating laser can be eliminated in the interests of simplicity, reliability and reduced cost at the expense of less perfect regulation of the cathode surface temperature.
A further understanding of the nature and advantages of the present invention may be realized by reference to the remaining portions of the specification and the drawings.
In broad terms, the microwave gun comprises a cathode 15, a resonant microwave cavity 20, a momentum analyzer (momentum filter) 25, and a first laser 30, also referred to as the pre-pulse laser. Some embodiments include a second laser 35, also referred to as the auxiliary laser. Pre-pulse laser 30 and optional auxiliary laser 35 are the additional components that address the backstreaming electron problem. Although a thermionic cathode is used in specific embodiments, other cathodes (e.g., photoemissive cathodes, or laser-assisted thermionic cathodes, or field-emission cathodes) where the current density depends on the temperature of the emitting surface can be used.
Other possible applications that could benefit from use of the invention include radiotherapy linacs that can operate with a broader energy spread and hence do not need the momentum analyzer, or guns using photocathodes in which the illuminating laser pulse is sufficiently short as to limit the bunch length and energy spread without the use of the momentum filter.
Cavity 20 is cylindrical, having opposed end walls 40 and 45, and a peripheral side wall 50. Cathode 15 is mounted generally centrally along end wall 40 on a supporting structure 55, and end wall 45 is formed with a central exit aperture 60 in communication with the beam transport to momentum analyzer 25. A waveguide 65 communicates with the cavity interior through an inlet port 70, and couples to a source of microwave power (not shown). Momentum analyzer 25 includes a magnet (not shown) and a momentum analyzing slit 75 located within an evacuated chamber in the magnetic field region. An auxiliary heater 80 provides heat to the back surface of cathode 15, and cooperates with pre-pulse laser 30 and auxiliary laser 35 as will be described below. The auxiliary heater can be an incandescent filament or a laser.
In operation, cathode 15 is heated, and microwave power is supplied to the gun as microwave pulses. The microwave pulses are typically of a few microseconds in duration at intervals of several or tens of milliseconds, with the microwave frequency normally in the range of 1-10 GHz (wavelength in the range of 3-30 cm). Cathode 15 emits electrons, which are accelerated by the microwave field in cavity 20, pass through exit aperture 60, and enter momentum analyzer 25. Those electrons having energies in a particular energy range exit the momentum analyzer for their intended use. It is noted that the present invention does not require the use of a momentum analyzer for those applications, such as those outlined above, where a narrow range of electron energies is not needed.
In a representative embodiment, the magnet in momentum analyzer 25 is configured to cause an electron entering the momentum analyzer to undergo approximately 270° of deflection prior to exiting the momentum analyzer. Electrons of different energies are dispersed laterally, and momentum analyzing slit 75 allows electrons within a particular range to pass while blocking electrons outside the range.
While the particulars of the cavity structure are not part of the invention, it is noted that end wall 40 carries an inwardly extending nosepiece 85 surrounding cathode 15 and end wall 45 carries an inwardly extending, toroidal nosepiece 90 surrounding exit aperture 60. Nosepiece 85 is shaped to define a generally frustoconical surface surrounding cathode 15, and serves to shape the electric field surrounding cathode 15 in a manner that minimizes the space-charge induced emittance growth of the electrons that are emitted from the cathode. Nosepiece 85 and nosepiece 90 also have the effect of increasing the electric field to which the electrons are subjected.
According to a further optional refinement, supporting structure 55 positions cathode 15 at a location along cavity wall 40 in a manner that provides thermal isolation while maintaining cathode 15 at the same RF voltage as the cavity wall. To accomplish this, end wall 40 carries a half-wavelength coaxial transmission line (“stub”) extending axially outward from a first (cavity) end at the cavity wall to a second (termination) end at which the stub is shorted. Cathode 15 is physically located at the cavity end, but the mounting is at the termination end.
Overview of Structure and Operation of Pre-Pulse Laser 30 and Auxiliary Laser 35
Pre-pulse laser 30 and auxiliary laser 35 perform separate functions, and as alluded to above, auxiliary laser 35 is not needed in all embodiments. However, the description that follows will describe an embodiment with the two lasers. Pulsed beams from the two lasers are directed to the front face of cathode 15. The beams are directed along separate paths and encounter a beamsplitter 95. In the particular geometry shown, the transmitted component of pre-pulse laser 30's beam and the reflected component of auxiliary laser 35's beam are directed to the cathode. The reflected component of pre-pulse laser 30's beam and the transmitted component of auxiliary laser 35's beam are directed to a beam dump 100. The beams from pre-pulse laser 30 and auxiliary laser 35 are directed through respective shaping screens 105 and 110. An optical window 115 allows the beams to pass into the evacuated gun.
As can be seen in
Pre-pulse laser 30 can have any wavelength, so long as the cathode surface has adequate emissivity (say >0.5) at that wavelength. A pulsed, solid state infrared laser with a pulse length on the order of 0.1-1.0 microseconds and a pulse energy on the order of 0.01-1.0 joules, could provide the thermal input needed for operation of microwave guns with average current outputs on the order of 100-1000 milliamps. Shaping screen 105's purpose is to shape and focus the beam as required to uniformly illuminate the surface of the cathode during the pulse. The particular form of shaping screen 105 is typically derived from thermal scans of the cathode surface taken under the conditions in which the cathode will be operated.
As can also be seen in
Auxiliary laser 35 should have a photon energy below the value needed to induce photoemission, as this laser is intended only to facilitate local control of the cathode temperature, and not to contribute to emission. Auxiliary laser 35 should have a pulse length equal to the length of the applied microwave pulse, and can have a pulse energy on the order of 0.1-1.0 joules. Screen 110 shapes the laser beam as required to control the optical power density as a function of position on the surface of the cathode.
Since both laser beams are pulsed beams, suitable mechanisms are provided to modulate the respective laser beams as required to control the optical power density on the front surface of cathode 15 as a function of time. In a representative embodiment, auxiliary laser 35 is provided with a separate modulator 120, which may be a Pockels cell. While the two laser pulses may be of generally commensurate energy, pre-pulse laser 30's pulse is much shorter, and therefore has a much higher peak power than auxiliary laser 35's pulse. Therefore, the energy of the pre-pulse laser is preferably controlled by changing the timing of its Q-switch or the voltage of its flash lamps.
Auxiliary heater 80 provides heat to the rear surface of the cathode to provide the steady state thermal input required to maintain the cathode at the desired operating temperature. In a typical embodiment, auxiliary heater 80 would provide on the order of 20-50% of the total power required to maintain cathode temperature. In some instances, the auxiliary heater can be dispensed with. For example, if 100 millijoule pulses are delivered at 100 Hz, this amounts to an average power of 10 watts, which may be sufficient to maintain the cathode temperature without the auxiliary heater.
Thermal Modeling and Additional Design Considerations
As described below, the invention exploits the linearity of the thermal diffusion equation and the characteristic dependence of surface temperature on time during and after illumination of the cathode surface to achieve a transient equilibrium state in which the increase in temperature at the cathode surface due to the backstreaming electrons and the power deposited by the second laser is balanced by the decay in surface temperature following illumination by the first pulsed laser.
For descriptive purposes it suffices to model cathode 15 as an opaque, uniform right circular cylinder as shown in
T (r, t) is the temperature as a function of time t and position r,
Cv is the specific heat per unit volume,
k is the thermal conductivity, and
∇2 is the Laplacian differential operator.
For the case in which the front surface of the cathode is uniformly illuminated by the first laser and radiation losses can be neglected, only the temperature variation along the axis of the cylinder needs to be considered, and only the one-dimensional form of Fourier's equation needs to be considered:
Cv·dT(r,t)/dt=−k·d2T(r,t)/dz2 (2)
For both the general three-dimensional case and the special one-dimensional case, Fourier's equation is linear in the temperature T (r, t), so that the general solution corresponding to the sum of all power sources and sinks and defined boundary conditions is equal, simply, to the sum of the individual solutions for each source.
In this model, the primary effect of the first laser pulse is to deliver a pulse of thermal energy equal to the product of the emissivity and optical energy of the pulse to the surface of the cathode at a rate equal to the product of the emissivity and the instantaneous power of the light pulse. The thermal energy deposited by such an optical pulse is confined to a surface layer of thickness approximately equal to δz˜(k·δt/Cv)1/2 where δt is the length of the optical pulse. For short light pulses and temperatures for which the power emitted from the surface as black body radiation can be neglected, the surface temperature increases approximately as the square root of the elapsed time, ending at a peak temperature equal approximately to the ratio of the deposited energy to the specific heat of the material contained in this surface layer.
At the termination of the laser pulse, the surface temperature begins to fall, decaying with time as the inverse square root of the time elapsed since the beginning of the pulse as the thermal energy deposited at the surface diffuses into the volume beneath the surface.
In further detail, the thermal power emitted as black body radiation can generally be neglected for laser pulses on the order of a microsecond in length and operating temperatures characteristic of the operation of dispenser and lanthanum hexaboride cathodes (1100-1400 degrees C.) in current microwave electron guns. From the solution of the one-dimensional Fourier equation for heat conduction, the rise in temperature δT (t0) at the surface of the cathode due to the deposition of a pulse of thermal energy Q in the time interval 0−t0 can therefore be approximated by:
δT(t0)˜(Q/A)/(4·sqrt(π·Cv·k·t0)) (3)
Where:
Q/A is the heat input per unit area,
Cv is the specific heat per unit volume, and
k is the thermal conductivity.
The maximum temperature rise δT0=δT (t0) occurs just at the end of the illuminating laser pulse. The temperature for times t>t0 decays monotonically with time as t−1/2 during the interval following the laser pulse. Although the magnitude of the temperature rise in this model depends on the cathode's thermal conductivity and specific heat as well as the thermal energy deposited by the illuminating laser, the rate of decay of temperature for a fixed temperature rise δT0=δT(t0) is independent of these variables, varying with time as:
It follows that the rate of decay of temperature with time is greatest for times t˜t0, decaying monotonically to zero for t>>t0.
Therefore, within the limits set by the available laser pulse energy and cathode emissivity, thermal conductivity and specific heat, the laser pulse energy and trigger time can be chosen to yield a rate of decay of temperature with time at the cathode surface equal, but opposite to the rate of increase in temperature with time at the beginning of the onset of electron emission, or at any subsequent time within the cathode current pulse.
The operation of the microwave guns described in U.S. Pat. No. 4,641,103 is most typically optimized when the temperature rise of the surface of the cathode is reduced to a minimum during the current pulse emitted by the cathode. Observation of gun operation with lanthanum hexaboride cathodes at 1400 degrees centigrade indicate that the energy deposited at the surface by backstreaming electrons is sufficient to increase the cathode current by nearly a factor of two during a 6-microsecond current pulse. Using the Dushman equation to estimate the increase in temperature required to generate this increase in emission, it can be inferred that the energy deposited by the backstreaming electrons typically heats the surface by the order of 50 degrees centigrade during such a current pulses resulting in a rate of rise of temperature on the order of:
(dT/dt)backstreaming electrons˜50° K/6 microseconds (i.e., ˜8.3·106° K/second)
Assuming a one joule, 1 microsecond laser pulse, 10 mm2 cathode area, and the approximate specific heat and thermal conductivity for lanthanum hexaboride:
Volume Specific Heat˜1 cal/(cm2·sec·° K)
Thermal Conductivity˜3.5·10−2 cal/(cm·sec·° K)
the rise in temperature at the start of the cathode current pulse can be compensated by triggering the pre-pulse laser to fire 10 microseconds prior to the onset of cathode emission.
Alternatively, since the rate of decay of temperature due to conduction of the initial thermal impulse into the bulk decreases monotonically with time, the timing of the illuminating laser pulse can be adjusted to minimize the variation of surface temperature at other points within the current pulse: for example, that the rise in surface temperature at the end of the pulse could with the same parameters be canceled by triggering the pre-pulse laser 4 microseconds prior to the onset of emission.
Since the rate of surface cooling due to conduction of the heat deposited by such a pulsed laser is not constant, but varies at the −3/2 power of the time since illumination by the laser, the attainment of constant cathode temperature during the current pulse requires that an additional means be provided to heat the surface of the cathode during the pulse at a rate equal to the difference between the rate of cooling due to conduction of the initial thermal pulse into the bulk and the rate of rise of temperature due to the backstreaming electrons. This additional thermal power input can most easily be secured by illuminating the surface of the cathode with a second laser whose power is modulated in time to keep the surface temperature constant. The spatial profile of this second laser beam can also be adjusted as required to maintain a more nearly constant rate of rise of surface temperature across the cross section of the cathode if the distribution of the backstreaming electrons varies with position.
It is seen from this description that the increase in surface temperature due to the backstreaming electrons in a pulsed microwave electron gun can be compensated by supplying part of the energy required to heat the cathode to operating temperature via a pulse of laser light triggered to illuminate the surface of the cathode in advance of the cathode current pulse and timed to yield a rate of surface cooling equal to the rate of surface heating due to the backstreaming electrons at the end of the current pulse, and a second laser pulse timed to overlap the cathode current pulse and modulated in time and spatial profile as required to minimize the net change in surface temperature during the current pulse.
The energy and timing of the first laser pulse can be estimated from the rate of rise of the surface of the cathode as deduced from the change in cathode emission during the pulse and the thermal conductivity and specific heat of the cathode material. Beginning with this estimate, the laser pulse energy and timing can be optimized during operation by adjusting these parameters to minimize the change in emission during the current pulse. The intensity of the laser light delivered to the cathode by the second laser can be optimized using a conventional feedback loop as the thermal power deposited at the surface by this second laser acts to increase the surface temperature more or less as the time integral of the power.
The spatial profile of the light delivered to the cathode surface by the second laser can be optimized either by trial and error through observation of the effects of differing spatial distributions on the temporal profile of the cathode current, or by use of a fast, imaging pyrometer to determine those areas of the cathode in which additional thermal input is required to maintain constant temperature.
Since certain applications may benefit from the use of an electron beam with a spatially varying current density, the second laser can also be used to modify the temperature profile on the surface of the cathode, and therefore the spatial profile of the emitted cathode current. The optimum spatial profile of the laser light needed for these applications can be determined either: (1) from a detailed, first principles solution of the equations of motion for the system, the electron optics used to transport the electrons emitted from the cathode to the system in which they will be used, and solution of the three-dimensional form of the Fourier heat transfer equation: (2) by use of a fast imaging pyrometer to visualize the effect of differing spatial laser profiles on cathode temperature; or (3) by empirical observation of the effects of variation of the spatial profile of the second pulsed laser beam on system performance.
Alternatively, it may be that certain applications with which this microwave gun will be used require only coarse stabilization of the temporal and spatial variations in cathode current density during the microwave pulse consistent with the simple t-3/2 decay in cathode surface temperature following the firing of the first laser pulse. For these less demanding applications, the second pulsed laser can be dispensed with in the interests of simplicity, reliability and reduced cost.
To avoid thermal runaway, the thermal conductivity of the components used to mount the cathode should be high enough to insure that the thermal energy deposited on the surface of the cathode by the first and second lasers and by the backstreaming electrons cannot heat the cathode to a temperature beyond its rated operating temperature. Provided that the power lost to conduction and black body radiation exceeds the power added by the two lasers and the backstreaming electrons, an auxiliary heater (conventional heater or laser) can be employed to provide a few watts additional power to the rear surface of the cathode to heat the cathode to the temperature required to sustain operation. As with the microwave gun described in U.S. Pat. No. 4,641,103, the power provided by this auxiliary heater can be maintained as part of a closed-loop feedback system to maintain the cathode at constant average temperature, or to maintain the cathode current at its specified operating value.
The typical operating parameters for such a temperature-stabilized microwave electron gun would be as follows:
While a single microwave cavity is shown and is used in specific embodiments, the invention is not limited to a single cavity. Thus, the notion of a “cavity” includes multi-cell cavities in which the electron beam is accelerated during passage through a sequence of cavities phased to optimize the net acceleration while reducing the probability that an electron will reverse direction and strike the cathode during the RF pulse. The term “cavity” simply specifies a resonant structure in which the active volume is enclosed by conducting boundary conditions which, by design and construction, achieve a high accelerating gradient in operation at the frequency of the RF source, and employ that gradient to accelerate a charged particle beam in some way.
This can include the use of the accelerating field to extract the electrons from the cavity as well as subsequently to accelerate these electrons; there is nothing in this definition of “cavity” which would exclude the use of the term to describe a cavity which consisted of two or more coupled “cells” in which the amplitude and phase of the fields in each cell were set by techniques well known in the art to values appropriate for the acceleration of the electrons emitted from the cathode, and the reduction of the probability that the accelerated electrons would reverse direction and strike the cathode.
Similarly, while a simple cylindrical cathode is shown, cathodes that emit beams with additional possible cross sections can be used. For example, annular electron beams have found a number of important uses in e-beam based sources of electromagnetic radiation, and there is also clearly interest in elliptical beams in which the beam height and width differ.
In conclusion it can be seen that the present invention provides elegant and effective techniques for stabilizing the temperature of the cathode in the face of backstreaming electrons.
While the above is a complete description of specific embodiments of the invention, the above description should not be taken as limiting the scope of the invention as defined by the claims.
This application claims priority to U.S. Provisional Patent Application No. 61/323,827, filed Apr. 13, 2010, entitled “Temperature Stabilized Microwave Electron Gun,” the entire disclosure of which is incorporated by reference herein for all purposes.
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