1. Field
The present teachings generally relate to the field of plasma containment and more particularly, to systems and methods for establishing a stable plasma in a relatively compact containment chamber.
2. Description of the Related Art
Nuclear fusion occurs when two relatively low mass nuclei fuse to yield a larger mass nucleus and reaction products. Because a substantial amount of energy is associated with the reaction products, controlled nuclear fusion research is an ongoing process with efficient power generation being one of the important goals. For fusion to occur, two nuclei need to interact at a nuclear level after overcoming the mutually repulsive Coulomb barrier. Different methods can be used to promote such an interaction.
One widely-used method of promoting the fusion process is to provide a volume of plasma having the fusable ions at sufficient density and temperature. Such a plasma needs to be contained sufficiently long enough to allow the fusion reaction to occur. Preferably, such a containment substantially isolates the plasma from the surrounding environment to reduce heat loss.
One way to contain the fusionable plasma is to use magnetic fields to “pinch” and restrict the plasma to certain volumes. One magnetic confinement design commonly referred to as a “tokamak” restricts the plasma in a donut shaped (toroid) volume. Because many conventional magnetically confined fusion devices are geared toward power production, confinement volumes are designed to be large. Consequently, such large devices and various supporting components can be prohibitively complex and/or expensive to operate in widespread applications.
The foregoing drawbacks can be overcome by a containment method that enhances stability. Such a plasma can be designed and operated by determining a stable energy state of the system without imposing a quasi-neutrality condition; a contained plasma that includes a substantial induced electrostatic field will contribute significantly to the stability of the plasma. Compact devices based on such contained plasmas can be used in different applications, such as a neutron generator, an x-ray generator, and a power generator.
One aspect of the present teachings relates to a method for designing a plasma containment device, including generating a characterization of the energy of a plasma system having a distribution of electrons and a distribution of ions. The characterization includes an energy term associated with a bulk electrostatic field induced inside the plasma by dissimilarities between the distribution of electrons and the distribution of ions. The method further includes determining an equilibrium state associated with the characterization of the energy of the plasma system. The method further includes determining one or more plasma parameters associated with the equilibrium state.
In a further aspect, the present invention relates to a method of plasma containment, including providing a plasma system, comprising a plurality of charged first particles and a plurality of charged second particles, and creating a dissimilarity between the overall distributions of the first and second particles. In one embodiment, the method includes restricting the plasma to a first beta value, second beta value, and first particle skin depth, the first and second beta values depending on factors comprising average particle number density, average plasma temperature, and strength of a magnetic field established in the plasma. In one embodiment, the inverse of the first beta value is between approximately 0 and 22 and the inverse of the second beta value is between approximately 0 and 3, with a first particle skin depth of between 1 and 2 in a cylindrical configuration.
In a further aspect, the present invention relates to a method of plasma containment, including providing a plasma comprising a plurality of first particles and a plurality of second particles, confining the first particles substantially to a first volume, and confining the second particles substantially to a second volume, with the second volume being larger than and encompassing the first volume. In one embodiment, movement of the first particles creates an electric current, and confining the first particles substantially to the first volume comprises establishing a magnetic field in the plasma substantially perpendicular to the direction of the current. In a further embodiment, confining the second particles substantially to the second volume comprises separating the bulk distributions of the first particles and the second particles such that a bulk electrostatic field is created in the plasma between the first particles and the second particles.
In a further aspect, the present invention relates to a method of plasma containment, including providing a plasma comprising a plurality of charged first particles and a plurality of charged second particles, with the first particles establishing a current by acting as charge carriers in the plasma, and imposing a magnetic field on the plasma, the magnetic field being oriented substantially perpendicular to the current and acting on the first particles to create a dissimilarity in distributions between the first particles and the second particles within the plasma. In one embodiment, the first particles comprise electrons and the second particles comprise ions. In another embodiment, the first particles comprise ions and the second particles comprise electrons. In a further embodiment, the plasma is contained within a substantially cylindrical volume, the volume defining an axial direction and an azimuthal direction, which may constitute part of a toroid. The current may flow in a combined axial-azimuthal direction with the magnetic field oriented in a combined aximuthal-axial direction. The current flow and magnetic field may be oriented spirally.
In a further aspect, the present invention relates to a method of plasma containment, including providing a plasma comprising a plurality of charged first particles and a plurality of charged second particles, the first particles being charge carriers of a current in the plasma, establishing a magnetic field in the plasma that electromagnetically influences the position of the first particles more than it influences the position of the second particles, confining the first particles substantially to a first volume under the influence of the magnetic field, and maintaining at least a portion of the second particles outside the first volume. The position of the first particles may be electromagnetically influenced through a screw pinch. A bulk electrostatic field may be established within the plasma, and confining the second particles to a second volume (the first volume being smaller than and contained within the second volume), under the influence of the bulk electrostatic field.
FIGS. 15A-C show various scales of plasma containment facilitated by electrostatic fields induced by separation of charges;
These and other aspects, advantages, and novel features of the present teachings will become apparent upon reading the following detailed description and upon reference to the accompanying drawings. In the drawings, similar elements have similar reference numerals.
The present teachings generally relate to systems and methods of plasma confinement at a relatively stable equilibrium. In one aspect, such a plasma includes a substantial internal electrostatic field that facilitates the stability and confinement of the plasma.
For the purpose of description, the plasma 100 can be characterized as a two-fluid system having an electron fluid and an ion fluid. It will be understood that the ion fluid can involve ions based on the same or different elements and/or isotopes. It will also be understood that the collective fluid-equation of characterization of the plasma herein is simply one way of describing a plasma, and is in no way intended to limit the scope of the present teachings. A plasma can be characterized using other methods, such as a kinetic approach, as will be apparent to those skilled in the art in light of this disclosure.
As shown in
As further shown in
As described herein, formation of such electrostatic fields within the plasma 100 contributes to the energy of the plasma system. Determining a relatively-stable energy state of such a system yields plasma parameters, including selected ranges of a plasma dimension L, that are substantially different than that associated with conventional plasma systems. It is generally known that static electric fields in a plasma typically do not exist over a distance substantially greater than the Debye length. They are shielded out because of rearrangements of electrons and ions. This, however, is in the absence of external forces. In the present disclosure described herein, the plasma dimension L is generally greater than many Debye lengths; however this is permitted because of the presence of external forces due to, for example, presence of magnetic fields.
In the description below, various embodiments of plasma systems are described as cylindrical and toroidal systems. In the present disclosure a cylindrical geometry is used for a simplified description, and is not to be construed as limiting in any manner. Because at least some of the effects described herein depend on the scale of the contained plasma, many arbitrary shapes of a contained plasma can be used in connection with the present disclosure. As an example, the plasma 100 in
One aspect of the present teachings relates to a method for determining a plasma state that is relatively stable and wherein such stability is facilitated by formation of a relatively substantial internal electrostatic field.
One way to characterize the energy of the plasma system is to use a two-fluid approach without the quasi-neutrality assumption. In conventional approaches, quasi-neutrality is assumed such that electron and ion density distributions are substantially equal. In contrast, one aspect of the present teachings relates to characterizing the two-fluid system such that the electron and ion densities are allowed to vary independently substantially throughout the plasma. Such an approach allows the two fluids to be distributed differently, and thereby induce a bulk electrostatic field at an equilibrium state of the plasma.
For a plasma contained at least partially by a magnetic field, the energy U of the system can be expressed as an integral of a sum of an E-field energy term, a B-field energy term, kinetic energy terms of the two fluids, and energy terms associated with pressures of the two fluids. Thus,
where E represents the electric field strength, εo represents the permittivity of free space, B represents the magnetic field strength, μo represents the permeability of free space, the summation index and subscripts s denote the species electrons e or ions i, ms represents the mass of the corresponding species, ns represents the particle density of the corresponding species, us represents the velocity of the corresponding species, ps represents the pressure of the corresponding species fluid, and dV represents the differential volume element of the volume of plasma.
For the purpose of description herein, it will be understood that terms “particle density,” “number density,” and other similar terms generally refer to a distribution of particles. Terms such as “electron density” and “electron number density” generally refer to a distribution of electrons. Terms such as “ion density” and “ion number density” generally refer to a distribution of ion. Furthermore in the description herein, terms such as “average particle density” and “average number density” are used to generally denote an average value of the corresponding distribution.
One way to further characterize the plasma is to treat the system as being a substantially collisionless and substantially fully-ionized plasma in a steady-state equilibrium. Moreover, each species of the two fluids can be characterized as substantially obeying an adiabatic equation of state expressed as
ps=Csnsγ (2)
where the Cs represents a constant that can be substantially determined by a method described below, and γ represents the ratio of specific heats of the two species.
Temperatures associated with the two species can be determined through an ideal gas law relationship
ps=nskTs (3)
where k represents the Boltzmann's constant. Furthermore, both species are assumed to be substantially Maxwellian.
One way to further characterize the plasma is to express, for each species, a substantially collisionless, equilibrium force balance equation as
msns(us·∇)us=qsns(E+us×B)−∇ps (4)
where ms represents the particle mass of species s, qs represents the charge, us represents the fluid velocity, and where the anisotropic part of the stress tensor can be and is ignored for simplicity for the purpose of description.
One way to further characterize the plasma is to express, for the system, Maxwell's equations as
As is known, Equation (5) is one way of expressing Poisson's equation; Equation (6) is one way of expressing Ampere's law for substantially steady-state conditions; Equation (7) is one way of expressing the irrotational property of an electric field which follows from Faraday's Law for substantially steady-state conditions; and Equation (8) is one way of expressing the solenoidal property of a magnetic field.
As is also known, Maxwell's equations assume conservation of total charge of a system. Accordingly, one can introduce a dependent variable Q defined as
∇·Q=ne (9)
to substantially ensure electron conservation by adopting appropriate boundary conditions in a manner described below. The electron density ne can further be characterized as obeying a relationship ne>0.
One way to determine a relatively stable confinement state of a plasma system is to determine an equilibrium state that arises from a first variation of the total energy of the plasma system as expressed in Equation (1) subject to various constraints as expressed in Equations (2)-(9). For the present invention, total energy may be defined as the combination of energy associated with pressure due to the temperature of the plasma particles, in this case ions and electrons, energy stored in the net electric field, energy stored in the net magnetic field, and kinetic energy associated with the movement of the plasma particles, in this case ions and electrons. In one such determination, the pressure term in Equations (1) and (4) can be eliminated by using Equation (2). The resulting constraints can be adjoined to the resulting energy expression U by using Lagrange multiplier functions. Such a variational procedure generally known in the art can result in a relatively complex general vector form of nonlinear differential equations.
One way to simplify the variational procedure without sacrificing interesting properties of the resulting solutions is to perform the procedure using cylindrical coordinates and symmetries associated therewith. The cylindrical symmetries can be used to reduce the independent variables of the system to one variable r. Accordingly, dependent variables of the system can be expressed as ni, ne, Er, Bz, Bθ, Q, uiz, uiθ, uez, and ueθ, where subscripts i and e respectively represent ion and electron species. The first six are state variables. Because derivatives of the last four (velocity components) do not appear in Equations (11A)-(11P) they can be treated as control variables in a manner described below.
Applying the cylindrical symmetries to the plasma system (where constraints ∇×E=0 and ∇·B=0 of Equations (7) and (8) are substantially satisfied identically), cylindrical coordinate expressions associated with Equations (4)-(6) and (9) can be adjoined to U of Equation (1) using Lagrange multiplier functions Mi, Me, ME, Mz, Mθ, and MQ. As the name implies, variations of the control variables may be considered as producing variations in the state variables as well as in the Lagrange multiplier functions.
The variation of U leads to first-order differential equations for the state variables and for the Lagrange multiplier functions, and to algebraic equations for the control variables. Such equations can conveniently be expressed as equations in dimensionless form using the following replacements: r→rΛe, us→Usc, n→N0n, E→EeN0Λe/ε0, B→BeN0Λeμ0c. Cs→Csmec2N01−γ, ps→psmeN0c2, Q→QΛe and T→Tsk/mc2, where c represents the speed of light, N0 represents the average particle density, e represents the magnitude of the electron charge, and Λe represents the electron skin depth expressed as
Λe=(me/μoN0e2)1/2 . (10)
One system of equations that follows from the foregoing energy variation method can be expressed as
One set of boundary conditions (at r=0 and r=a, where a is defined as an outer boundary in
In one implementation of a method for determining a stable equilibrium of the foregoing cylindrical plasma system, input parameters (expressed in dimensional form) for solving the system of equations (Equations (11A-P)) include the cylindrical radius a, the average particle number density N0 substantially equal for both species, the axial magnetic field at the boundary a such that Bz(a)=B0, the net axial current I, and a temperature value T0 for both electrons and ions that is the temperature taken at that value of r at which ns=N0. Using these input parameters, one can determine that Bθ(a)=μ0I/(2πa).
Furthermore, the values of Cs can be determined by combining the adiabatic equation of state from Equation (2) and the ideal gas law from Equation (3) so as to yield Cs=ns1−γkTs. Thus, Cs=N01−γkT0 when evaluated at the value of r where ns=N0 and Ts=T0. The electron and ion average temperatures may be different, which would result in different values of Ci and Ce. For the examples of the present disclosure, they are taken to be substantially the same, i.e., T0. Such a simplification for the purpose of description should not be construed to limit the scope of the present teachings in any manner.
Another useful set of input parameters can be obtained by replacing B0 with a plasma beta value defined as β=N0kT0/(B02/2μ0) and by replacing I with another beta value a α=N0kT0/(Bθ(a)2/2μ0), where I=2πaBθ(a)/μ0. Note that 1/β=0 corresponds substantially pure Z-pinch, and 1/α=0 corresponds to a substantially pure theta-pinch. A screw-pinch corresponds to substantially nonzero values for both 1/α and 1/β.
The foregoing energy variational method yields a description of the plasma system by twelve first-order coupled nonlinear ordinary differential equations, four algebraic equations, and one inequality condition (ne>0), with sixteen unknowns. Numerical solutions to such a system of equations can be obtained in a number of ways. Solutions disclosed herein are obtained using a known differential equation solving routine such as BVPFD that is part of a known numerical analysis software IMSL.
The plasma 140 defines a first cylindrical volume 150 extending from the Z-axis to r=Y, and a second cylindrical volume 152 extending from the Z-axis to r=a. The first volume 150 generally corresponds to a region of the plasma 140 where the first species of the two fluids is distributed as n1(r). The second volume 152 generally corresponds to a region of the plasma 140 where the second species of the two fluids is distributed as n2(r).
In general, the first and second species are distributed such that
That is, the first region 150 has more of the first species than the second species, and the portion of the second region 152 outside of the first region has substantially none of the first species. As Equation (12C) shows, the total number of particles in the two species is substantially the same in one embodiment.
In some embodiments, substantially all of the first species is located within the first region 150 such that r=Y defines a boundary for the first species. Consequently, the region Y<r<a has substantially none of the first species, and is populated by the second species by an amount ΔN. Since the total numbers of the first and second species are substantially the same in one embodiment, the value of ΔN is also representative of the excess number of the first species relative to the second species in the first region 150.
In some embodiments, as described below in greater detail, the first species can be the electrons, and the second species the ions when a plasma is contained within one or more selected ranges of value for the boundary r=Y. In other embodiments, as also described below in greater detail, the first species can be the ions, and the second species the electrons when the plasma is contained in one or more other selected ranges of value for the boundary r=Y.
As shown in
As described below in greater detail, when the radial dimension of the plasma is selected in certain ranges, motion of one species relative to the other species can be enhanced and thereby be more subject to the magnetic pinching force. Thus, as shown in
As shown in
One can see that when the distance R is relatively large compared to a, such as in a high aspect ratio (R/a) toroid, a given segment of the toroid geometry can be approximated by the cylindrical geometry. Thus, one can obtain design parameters using a cylindrical geometry, and apply such a solution to designing of a toroidal device. As is known in the art, such a cylindrical approximation provides a good base for a toroidal design. One way to correct for the differences between the toroidal and cylindrical geometries is to provide a corrective external field, often referred to as a vertical field that inhibits the plasma toroid radius R from increasing due to magnetic hoop forces, to confine the plasma.
Thus as shown in
The foregoing analysis of the cylindrical plasma includes a one-dimensional (r) analysis using the energy variation method. As described above in reference to
One aspect of the present teachings relates to a scale of a contained plasma having a substantial electrostatic field induced therein. Various results of the foregoing energy variational procedure are described in the context of cylindrical symmetry. It will be appreciated, however, that such results can also be manifested in other shapes of contained plasma having a similar scale.
The foregoing input parameters result in a contained plasma where the electrons are pinched by magnetic forces thereby giving rise to electron-ion charge separation. Consequently, the electrons are distributed substantially within the inner region of the cylinder (first region 150 in
It will be appreciated that while the magnetic field provides an initial confinement mechanism for the plasma, the internally-produced electric field plays an important and substantial role in establishing a stable plasma equilibrium. The force profiles shown in
As shown in
As further shown in
One aspect of the present teachings relates to a plasma system having an induced separation of charges, as shown by the electron and ion distributions 250 and 254, thereby causing formation of the radially directed electric field profile 252 that substantially overlaps with the plasma volume. Such a coverage of the induced electrostatic field can be achieved in contained plasma systems where the boundary Y for electrons has a dimension on the order of the electron scale length Λe.
For a system to lie within an energy well sufficiently deep to provide a robust confinement for one embodiment, the cylinder radius can lie within a range near the value of the electron scale length (skin depth) Λe In the example embodiment described above in reference to
A relatively large radius configuration (e.g., Y=6Λe) can result in a substantial electric field being induced near the outer region of the plasma cylinder. An energy well associated with such a configuration can be relatively shallow when compared to the Y≈1.2Λe case. Also, a relatively small radius configuration (e.g., Y=0.3Λe) can result in confinement being lost.
Thus in one embodiment, a plasma confinement that is facilitated by the induced electrostatic field has a value of Y that is in a range of approximately 1 to 2 times the electron scale length Λe. In one embodiment, a value of Y around 1.2Λe appears to provide a near optimal confinement condition. For a plasma with N0=1019/m3 (as with the example plasma of
The plasma is contained such that energy and/or particle loss(es) from the plasma to a wall defining a containment volume is reduced. One way to achieve such energy/particle loss reduction is to reduce the number of plasma particles coming into contact with the wall. As shown in
As described above, for a plasma containment design where a=3Λe, the outer radius a is approximately 5.1 mm for the Y=1.2Λe case. For such a system, a wall can be positioned at a location r>5.1 mm and still allow construction of a relatively small containment device. Moreover, the ion number density at r>5.1 mm (3Λe) is substantially lower than the 0.1% level described above. Thus, the number of ions coming into contact with the wall at r>5.1 mm and transferring energy thereto and/or interacting therewith is reduced even more.
The example plasma described above in reference to
The present disclosure reveals substantial electric fields due to excess electrons in the r<Y region and ions being substantially the only species in the r>Y region. As described above, numerical solutions can be obtained by solving Equations (11A)-(11P) for r<Y and substituting Y for a in the boundary conditions. One can solve the modified set (for ions) for r>Y and replacing 0 by Y in the boundary conditions and then matching the solutions of the two sets at r=Y. In one embodiment, the number density of the magnetically bound species becomes substantially zero at r=Y.
In one embodiment, accomplishing such a matching process can place an additional restriction on the input or control parameters that can be expressed in terms of 1/α and 1/β. For example, in the cylindrical coordinate treatment of the Z-pinch embodiment, 1/α, which can be obtained from N0, T0, and B0, is approximately 2 (for typical fusion plasma parameter values). A more precise value of 1/α can be expressed as a slowly varying function of T0 and n0. For the example cylindrical geometry, an approximate value can be obtained from an example contour plot of 1/α as a function of Y/Λe and temperature T, such as that of
The example plasma described above in reference to
For the theta-pinch example, an outer diameter a of approximately 3Λe is used. Furthermore, input parameters N0=1019/m3, T0=104 keV, 1/α=0, and 1/β=20.5 are used. The corresponding electron scale length Λe=(me/μoN0e2)1/2 is approximately 1.7 mm.
Based on the foregoing example inputs,
The foregoing example theta-pinch confinement results in the value of Y being approximately 2.04 mm. Thus, a theta-pinched plasma with a confinement dimension on the order of the electron scale length Λe can provide the various advantageous features described above in reference to the Z-pinched plasma system.
As previously described, a screw-pinch can be achieved by a combination of Z and theta pinches. Thus, an energy variational analysis similar to the foregoing can be performed with 1/α≠0 and 1/β≠0 to yield similar results where a substantial electrostatic field is induced by separation of charges. Furthermore, a screw-pinched plasma with a confinement dimension on the order of the electron scale length Λe can provide similar advantageous features described above in reference to Z and theta pinched plasma systems. Screw-pinch magnetically confined plasmas are generally regarded as more stable than simple Z- or theta-pinches. It is expected that screw-pinch embodiments of the present teachings will share the various features disclosed herein.
As also described, magnetically confining a plasma in a dimension on the a order of the plasma's electron scale length results in separation of charges, thereby inducing a substantial electrostatic field over a substantial portion of the plasma volume. Such an electric field can be characterized so as to correspond to a depth of an energy well associated with a stable equilibrium. Moreover, the energy well depth is expected to be relatively deep when the electron fluid radius Y is in a range of approximately 1-2Λe. Such relatively deep energy well of the equilibrium provides a relatively stable confined plasma. Such stability of a confined plasma at a value of Y of approximately 1-2 Λe, however, does not preclude a possibility that magnetic confinement at larger values of Y can have its stability facilitated significantly by the induced electrostatic field.
One aspect of the present teachings relates to a magnetically confined and relatively stable equilibriated plasma at different dimensional scales. FIGS. 15A-C show electron and ion distributions for different plasma sizes. While the larger sized plasma systems may not yield equilibria that are as stable as the case where Y=1-2 Λe, such equilibria may nevertheless have sufficient stabilities that are facilitated by the electric field.
In various plasma embodiments, the electric field coverage scales (304, 310, 316) are generally similar, and can be on the order of few electron scale lengths. Thus, one way to characterize a role of the electrostatic field in the stability of the plasma is to consider the electric field as a layer formed near the surface of the plasma volume. In systems where a plasma volume dimension (e.g., radius a in cylindrical systems) is on the order of the E-field layer “thickness” (such as the system of
In systems where a plasma volume dimension is substantially larger than the E-field layer “thickness” (such as the systems of
One aspect of the present teachings relates to a plasma having a substantially larger scale length (skin depth) than that of plasmas where the induced electrostatic field is on the order of an electron scale length (electron skin depth).
In such a role-reversed plasma, ions act as charge carriers, thereby being subject to magnetic confinement. The value of a for the ions-moving plasma would be many times that for the electrons-moving plasma because of the much larger ion skin depth Λion=(mion/μoN0e2)1/2. For plasmas having a similar average density value, the ratio of Λion/Λe=(mion/me)1/2. For deuterium, the ratio Λion/Λe is approximately 61. Thus, a plasma having moving ions would have a volume of approximately 612=3700 times that of the similar electrons-moving plasma, all else being substantially the same. The energy variational method described herein can be modified readily for analysis, and a resulting plasma system likely would be sufficiently large to allow power production.
As described above in connection with
As described above in connection with
As described above in connection with
Being a charge carrier in the plasma can be characterized in different ways. One way is to say that charge carriers cause a current in the plasma. Another way is to say that charge carriers undergo a bulk motion in the plasma. Yet another way is to say that charge carriers flow in the plasma.
In one embodiment, both the electrons and the ions can act as charge carriers. That is, both the electrons and the ions can contribute to the current, undergo bulk motions, and flow in the plasma. A difference in the degrees of a current-producing characteristic of the two species can give rise to one species being confined magnetically more than the other. Such a difference in the magnetic confinements of the two species can induce a charge separation that causes formation of an electrostatic field in the plasma.
As previously described, the Z- and theta-pinches can be combined to yield a screw-pinch. Thus, the Z and theta pinch devices of
As shown in
The plasma 372 contained in the foregoing manner can undergo a nuclear fusion reaction that can yield neutrons, x-rays, power, and/or other reaction products. Some of the possible reaction configurations and products for an example deuterium-tritium (DT) reaction at various example operating conditions are summarized in Tables 1-3.
Table 1 summarizes various dimensions associated with an electron-scaled high aspect ratio toroidal system at various particle densities. Quantities associated with Table 1 are defined as follows: n=average particle density; Λ=electron scale length; Y=electron fluid boundary radius=set to 1.5Λ; a=toroid's minor radius=ion fluid boundary radius=set to 2.5Y; R=toroid's major radius=set to 20a; V=toroid's volume=2π2Ra2.
Table 2 summarizes various neutron production rate estimates with the system of Table 1 at various temperatures. Quantities associated with Table 2 are defined as follows: T=plasma temperature; σv=reaction rate; neutron rate=n2(σv)V/4. These reaction rate and neutron rate expressions are well known in the art.
Table 3 summarizes various power production estimates with the system of Table 1 at various temperatures for a deuterium-tritium device. Quantities associated with Table 3 are defined as follows: T=plasma temperature; power associated with charged particles=(nDnTσv)(5.6×10−13) (Watts). The power expression is well known in the art.
As an example from Tables 1-3, not to be construed as limiting in any manner, consider a plasma system having a DT fuel confined in a high aspect ratio toroidal chamber. An average number density n of approximately 1020 m−3 corresponds to an electron scale length Λ of approximately 0.0532 cm. Setting Y=1.5Λe=0.080 cm, the minor radius a at 2.5Λe=0.20 cm, the major radius R at 20a =4 cm results in a volume V of approximately 3.13 cm3.
Operating such a plasma at a temperature of approximately 5 keV (where the reaction rate is approximately 1.30×10−17) can yield approximately 1.02×1011 neutrons per second. Neutron fluxes of such an order in such a compact device are useful in many areas such as antiterrorist materials detection, well logging, underground water monitoring, radioactive isotope production, and other applications.
Operation of such a DT-fueled plasma can also yield high intensity soft x-rays having energies in a range of approximately 1-5 keV. Such x-rays from such compact device are useful in areas such as photolithography. In one embodiment, the soft x-rays are produced from the plasma even if fusion does not occur.
From Tables 1-3, one can see that the example operating parameters of 1020 m31 3 average number density at temperature of 5 keV yields a power output of approximately 57 mW. Power output can be increased dramatically by varying different plasma parameters. As previously described, the example plasma solution in reference to
As a relatively conservative estimate for a possible power increase, a change in temperature by a factor of approximately 20 yields a plasma temperature of approximately 100 keV, where power output is approximately 3.72 W when n=10 20 m31 3. Additionally, as described above in connection with FIGS. 15A-C, electrostatic field facilitated stable plasmas can be formed with an increased volume. Thus, scaling both major and minor radii of the high aspect ratio toroid by a factor of 10 increases the volume by a factor of 103. Thus, because the power output is proportional to the volume of the plasma, the foregoing example 3.72 W output device can be scaled so as to produce several kilo-Watts of power. Such a device has a major radius of approximately 40 cm, which is still a relatively compact device for a power generator.
Various example plasma devices described herein can be operated by including an example start-up process that facilitates formation of a stable and confined plasma. The example start-up process is described in context of a plasma device having a toroidal geometry where both toroidal (axial) and poloidal (azimuthal) magnetic fields play a substantial role in confinement. Similar start-up process generally applies to the Z, theta and screw pinch concepts described herein.
In one embodiment, a vacuum toroidal magnetic field is established by current-carrying toroidal field coils wound in the poloidal direction (such as that shown in
Thus, the foregoing example start-up process can bring the plasma into a parameter regime of substantial densities and temperatures that characterize the plasma environment. Subsequently, the plasma proceeds toward a stable, confined equilibrium configuration via relaxation processes with the concomitant development of a substantial, radial electrostatic field that provides confinement for the ions. Additional heating mechanisms such as radio frequency heating can be used to further increase the plasma temperature and hence the probability of fusion events occurring in the plasma environment.
Although the above-disclosed embodiments have shown, described, and pointed out the fundamental novel features of the invention as applied to the above-disclosed embodiments, it should be understood that various omissions, substitutions, and changes in the form of the detail of the devices, systems, and/or methods shown may be made by those skilled in the art without departing from the scope of the invention. Consequently, the scope of the invention should not be limited to the foregoing description, but should be defined by the appended claims.
This application is a divisional of U.S. patent application Ser. No. 10/804,520, filed 19 Mar. 2004, titled “Systems and Methods of Plasma Containment,” incorporated herein by reference. Application Ser. No. 10/804,520, in turn, claims priority benefit of U.S. provisional patent application No. 60/456,832, filed 21 Mar. 2003, titled “A Method of Obtaining Design Parameters for a Compact Thermonuclear Fusion Device,” incorporated herein by reference.
Number | Date | Country | |
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60456832 | Mar 2003 | US |
Number | Date | Country | |
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Parent | 10804520 | Mar 2004 | US |
Child | 11535307 | Sep 2006 | US |