Title: Formation of a field reversed configuration for magnetic and electrostatic confinement of plasma
Abstract: A system and method for containing plasma and forming a Field Reversed Configuration (FRC) magnetic topology are described in which plasma ions are contained magnetically in stable, non-adiabatic orbits in the FRC. Further, the electrons are contained electrostatically in a deep energy well, created by tuning an externally applied magnetic field. The simultaneous electrostatic confinement of electrons and magnetic confinement of ions avoids anomalous transport and facilitates classical containment of both electrons and ions. In this configuration, ions and electrons may have adequate density and temperature so that upon collisions they are fused together by nuclear force, thus releasing fusion energy. Moreover, the fusion fuel plasmas that can be used with the present confinement system and method are not limited to neutronic fuels only, but also advantageously include advanced fuels.
Patent Number: 6,891,911 Issued on 05/10/2005 to Rostoker, et al.
| Inventors:
|
Rostoker; Norman (Irvine, CA);
Binderbauer; Michl (Irvine, CA);
Garate; Eusebio (Irvine, CA);
Bystritskii; Vitaly (Irvine, CA)
|
| Assignee:
|
The Regents of the University of California (Oakland, CA)
|
| Appl. No.:
|
328674 |
| Filed:
|
December 23, 2002 |
| Current U.S. Class: |
376/128; 315/111.21; 376/130 |
| Intern'l Class: |
G21B 001/00 |
| Field of Search: |
315/11121,111.41,111.51,111.61
376/107,128,130,133,129,141
|
References Cited [Referenced By]
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| 4010396 | Mar., 1977 | Ress et al.
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| 4057462 | Nov., 1977 | Jassby et al.
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| 4065351 | Dec., 1977 | Jassby et al.
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| 4894199 | Jan., 1990 | Rostoker.
| |
| 6396213 | May., 2002 | Koloc.
| |
| 6664740 | Dec., 2003 | Rostoker et al.
| |
Other References
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Rostoker, N. et al., Self-colliding beams as an alternative fusion system
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Systems for Aneutronic Fusion, vol. 15, No. 2, pp. 105-120, 1992 Gordon and
Breach, Science Publishers S.A., U.K.
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American Institute of Physics, pp. 1425-1430.
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17, No. 3 (Sep. 1998), pp. 209-211.
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|
Primary Examiner: Lee; Wilson
Attorney, Agent or Firm: Orrick, Herrington & Sutcliffe LLP
Parent Case Text
CROSS-REFERENCE TO RELATED APPLICATION
This application is a continuation of U.S. Ser. No. 10/066,424, filed Jan. 31,
2002, now U.S. Pat. No. 6,664,740, which claims the benefit of provisional U.S.
application Ser. No. 60/266,074, filed Feb. 1, 2001, and provisional U.S. application
Ser. No. 60/297,086, filed on Jun. 8, 2001, which applications are fully incorporated
herein by reference.
Claims
1. A method of forming a magnetic field with field reversed configuration (FRC)
topology, comprising the steps of
energizing a plurality of field coils extending about a vessel,
forming a magnetic guide field extending axially within the vessel, the guide
field including first and second radial magnetic field components in spaced relation
to axially confine there between plasma injected into the vessel,
axially injecting plasma along the axial guide field and forming an annular plasma
layer within the vessel, the plasma comprising charged particles including a plurality
of electrons and a plurality of ions,
energizing a betatron flux coil concentric with a principle axis of the vessel
by running current through the coil,
increasing the current running through the coil causing a change in axial flux
in the interior of the coil,
creating an azimuthal electric field within the vessel due to the change in axial
flux,
rotating the annular layer of plasma within the vessel,
generating a current due to the rotating plasma,
creating a magnetic poloidal self-field surrounding the rotating plasma, wherein
field lines external to the annular plasma layer extend in the same direction as
field lines of the guide field and field lines internal to the annular plasma layer
extend in a direction opposite to the field lines of the guide field, and
increasing the self field to a magnitude at least comparable to the guide field
and sufficient to cause field reversal.
2. The method of claim 1 further comprising the step of magnetically connecting
open field lines of the guide field with field lines of the self field.
3. The method of claim 1 where in the step of rotating the annular layer of plasma includes
coupling the azimuthal electric field to the charged particles in the plasma,
and
accelerating the charged plasma particles in the annular layer due to ponderomotive
forces exerted on the particles by the azimuthal electric field.
4. The method of claim 1 wherein the step of forming the first and second radial
field components of the guide field includes increasing current running through
one or more coils at opposing ends of the plurality of field coils.
5. The method of claim 1 wherein the step of increasing the magnitude of the
self-field includes increasing the rotational energy of the annular plasma layer.
6. The method of claim 5 wherein the step of increasing the rotational energy
of the annular plasma layer includes increasing the rate of change of the current
running through the flux coil.
7. The method of claim 5 wherein the rotational energy of the annular plasma
layer is increased to a range of about 75 eV to 125 eV.
8. The method of claim 5 wherein the rotational energy of the annular plasma
layer is increased to about 100 eV.
9. The method of claim 1 further comprising the step of increasing the rotational
energy of the annular plasma layer to fusion relevant conditions.
10. The method of claim 9 wherein the rotational energy of the annular plasma
layer is increased to a range of about 100 keV to 3.3 MeV.
11. The method of claim 9 wherein the rotational energy of the annular plasma
layer is increased to about 200 keV.
12. The method of claim 9 further comprising the step of creating an electrostatic
well with in the vessel.
13. The method of claim 12 further comprising the step of manipulating the magnitude
of the guide field generated by the plurality of field coils to tune the magnitude
of the electrostatic well.
14. The method of claim 13 further comprising the step of injecting ion beams
of fusion level energy into the FRC and trapping the beams in betatron orbits within
the FRC.
15. The method of claim 14 wherein the injected ion beams are at an energy level
of about 100 keV to 3.3 MeV.
16. The method of claim 14 wherein the step of injecting and trapping the ion
beams further comprises the steps of
neutralizing the ion beams,
draining the electric polarization from the neutralized ion beams, and
exerting a Lorentz force due to the FRC on the neutralized ion beams to bend
the ion beams into betatron orbits.
17. The method of claim 16 further comprising the steps of magnetically confining
ions within the FRC and electrostatically confining electrons within the electrostatic well.
18. The method of claim 17 further comprising the step of forming fusion product ions.
19. The method of claim 18 further comprising the step of exiting the fusion
product ions from the FRC in an annular beam.
20. A method of forming a field reversed configuration magnetic field within
a chamber comprising the steps of
creating a magnetic guide field in a chamber by energizing a plurality of field
coils and mirror coils extending about the chamber,
injecting plasma into the chamber along the guide field,
creating an azimuthal electric field within the chamber causing the plasma to
rotate and form a poloidal magnetic self-field surrounding the plasma,
increasing the rotational energy of the plasma to increase the magnitude of the
self-field to a level that overcomes the magnitude of the guide field,
joining field lines of the guide field and the self-field in a magnetic field
having a field reverse configuration (FRC) topology, and
increasing the magnitude of the guide field to maintain the rotating plasma at
a predetermined radial size.
21. The method of claim 20 wherein the step of creating the azimuthal electric
field includes the step of energizing a betatron flux coil within the chamber and
increasing current running through the coil.
22. The method of claim 21 wherein the step of increasing the rotational energy
of the rotating plasma includes increasing the rate of change of the current running
through the coil.
23. The method of claim 22 further comprising the step of increasing the rate
of change of the current running through the flux coil to accelerate the rotating
plasma to fusion level rotational energy.
24. The method of claim 23 further comprising the step of creating an electrostatic
well within the chamber.
25. The method of claim 24 further comprising the step of tuning the electrostatic well.
26. The method of claim 25 wherein the step of tuning the electrostatic well
includes manipulating the magnitude of the guide field.
27. The method of claim 26 further comprising the steps of injecting ion beams
of fusion level energy into the FRC and trapping the beams in betatron orbits within
the FRC.
28. The method of claim 27 wherein the step of injecting and trapping the ion
beams further comprises the steps of
neutralizing the ion beams,
draining the electric polarization from the neutralized ion beams, and
exerting a Lorentz force due to the applied magnetic field on the neutralized
ion beams to bend the ion beams into betatron orbits.
29. The method of claim 28 further comprising the steps of magnetically confining
ions within the FRC and electrostatically confining electrons within the electrostatic well.
30. The method of claim 29 further comprising the step of forming fusion product ions.
31. The method of claim 30 further comprising the step of exiting the fusion
product ions from the FRC in an annular beam.
32. A method of forming a field reversed configuration magnetic field within
a reactor chamber comprising the steps of
energizing field coils positioned about a chamber to create a magnetic guide
field with axially extending field lines within the chamber,
injecting plasma comprising charged electron and ion particles into the chamber
along the field lines of the guide field,
rotating the plasma by creating an azimuthal electric field within the chamber
that applies ponderomotive forces to the charged particles,
forming a magnetic poloidal self field surrounding the rotating plasma due to
the current carried by the rotating plasma, and
increasing the rotational energy of the plasma to increase the magnitude of the
self-field to a level that overcomes the magnitude of the guide field causing field
reversal.
33. The method of claim 32 further comprising the step of increasing the magnitude
of the guide field to maintain the rotating plasma at a predetermined radial size.
34. The method of claim 33 wherein creating the azimuthal electric field includes
the step of increasing current running through a betatron flux coil concentric
with a principle axis of the chamber.
35. The method of claim 34 wherein the betatron flux coil includes a plurality
of coils wound in parallel.
36. The method of claim 32 wherein the step of increasing the rotational energy
of the plasma includes increasing the azimuthal electric field.
37. The method of claim 35 wherein increasing the azimuthal electric field includes
increasing the rate of change of the current running through the betatron coil.
38. The method of claim 37 further comprising the step of accelerating the rotating
plasma to fusion level rotational energy by increasing the rate of change of the
current running through the betatron coil.
39. The method of claim 32 wherein the step of increasing the energy of the rotating
plasma to cause field reversal includes accelerating the rotating plasma to a rotational
energy of about 75 to 125 electron volts.
40. The method of claim 38 wherein the rotating plasma is accelerated to a rotational
energy of about 100 kilo electron volts to 3.3 mega-electron volts.
41. The method of claim 38 further comprising the step of creating an electrostatic
well within the chamber.
42. The method of claim 41 further comprising the step of tuning the electrostatic well.
43. The method of claim 42 wherein the step of tuning the electrostatic well
includes manipulating the magnitude of the guide field.
44. The method of claim 43 further comprising the steps of injecting ion beams
of fusion level energy into the magnetic field with field reversal within the chamber
and trapping the beams in betatron orbits within the chamber.
45. The method of claim 44 wherein the injected ion beams are at an energy level
of about 100 kilo electron volts to 3.3 mega-electron volts.
46. The method of claim 44 wherein the step of injecting the ion beams further
comprises the steps of
neutralizing the ion beams,
draining the electric polarization from the neutralized ion beams, and
exerting a Lorentz force due to the FRC on the neutralized ion beams to bend
the ion beams into betatron orbits.
47. The method of claim 46 further comprising the steps of magnetically confining
ions within the FRC and electrostatically confining electrons within the electrostatic well.
48. The method of claim 47 further comprising the step of forming fusion product ions.
49. The method of claim 48 further comprising the step of exiting the fusion
product ions from the FRC in an annular beam.
Description
FIELD OF THE INVENTION
The invention relates generally to the field of plasma physics, and, in particular,
to methods and apparati for confining plasma. Plasma confinement is particularly
of interest for the purpose of enabling a nuclear fusion reaction.
BACKGROUND OF THE INVENTION
Fusion is the process by which two light nuclei combine to form a heavier
one. The fusion process releases a tremendous amount of energy in the form of fast
moving particles. Because atomic nuclei are positively charged—due to the
protons contained therein—there is a repulsive electrostatic, or Coulomb,
force between them. For two nuclei to fuse, this repulsive barrier must be overcome,
which occurs when two nuclei are brought close enough together where the short-range
nuclear forces become strong enough to overcome the Coulomb force and fuse the
nuclei. The energy necessary for the nuclei to overcome the Coulomb barrier is
provided by their thermal energies, which must be very high. For example, the fusion
rate can be appreciable if the temperature is at least of the order of 10
4
eV—corresponding roughly to 100 million degrees Kelvin. The rate of
a fusion reaction is a function of the temperature, and it is characterized by
a quantity called reactivity. The reactivity of a D-T reaction, for example, has
a broad peak between 30 keV and 100 keV.
Typical fusion reactions include:
where D indicates deuterium, T indicates tritium, α indicates a helium
nucleus, n indicates a neutron, p indicates a proton, He indicates helium, and
B
11 indicates Boron-11. The numbers in parentheses in each equation
indicate the kinetic energy of the fusion products.
The first two reactions listed above—the D-D and D-T reactions—are
neutronic, which means that most of the energy of their fusion products is carried
by fast neutrons. The disadvantages of neutronic reactions are that (1) the flux
of fast neutrons creates many problems, including structural damage of the reactor
walls and high levels of radioactivity for most construction materials; and (2)
the energy of fast neutrons is collected by converting their thermal energy to
electric energy, which is very inefficient (less than 30%). The advantages of neutronic
reactions are that (1) their reactivity peaks at a relatively low temperature;
and (2) their losses due to radiation are relatively low because the atomic numbers
of deuterium and tritium are 1.
The reactants in the other two equations—D-He
3 and p-B
11—are
called advanced fuels. Instead of producing fast neutrons, as in the neutronic
reactions, their fusion products are charged particles. One advantage of the advanced
fuels is that they create much fewer neutrons and therefore suffer less from the
disadvantages associated with them. In the case of D-He
3, some fast
neutrons are produced by secondary reactions, but these neutrons account for only
about 10 per cent of the energy of the fusion products. The p-B
11 reaction
is free of fast neutrons, although it does produce some slow neutrons that result
from secondary reactions but create much fewer problems. Another advantage of the
advanced fuels is that the energy of their fusion products can be collected with
a high efficiency, up to 90 per cent. In a direct energy conversion process, their
charged fusion products can be slowed down and their kinetic energy converted directly
to electricity.
The advanced fuels have disadvantages, too. For example, the atomic numbers of
the advanced fuels are higher (2 for He
3 and 5 for B
11) Therefore,
their radiation losses are greater than in the neutronic reactions. Also, it is
much more difficult to cause the advanced fuels to fuse. Their peak reactivities
occur at much higher temperatures and do not reach as high as the reactivity for
D-T. Causing a fusion reaction with the advanced fuels thus requires that they
be brought to a higher energy state where their reactivity is significant. Accordingly,
the advanced fuels must be contained for a longer time period wherein they can
be brought to appropriate fusion conditions.
The containment time for a plasma is Δt=r
2/D, where r is a minimum
plasma dimension and D is a diffusion coefficient. The classical value of the diffusion
coefficient is D
c=α
i2/τ
ie,
where α
i is the ion gyroradius and τ
ie is the
ion-electron collision time. Diffusion according to the classical diffusion coefficient
is called classical transport. The Bohm diffusion coefficient, attributed to short-wavelength
instabilities, is D
B=({fraction (1/16)})α
i2Ω
i,
where Ω
i is the ion gyrofrequency. Diffusion according to this
relationship is called anomalous transport. For fusion conditions, D
B/D
c=({fraction
(1/16)})Ω
iτ
ie≅10
8, anomalous
transport results in a much shorter containment time than does classical transport.
This relation determines how large a plasma must be in a fusion reactor, by the
requirement that the containment time for a given amount of plasma must be longer
than the time for the plasma to have a nuclear fusion reaction. Therefore, classical
transport condition is more desirable in a fusion reactor, allowing for smaller
initial plasmas.
In early experiments with toroidal confinement of plasma, a containment time
of
Δt≅r
2/D
B was observed. Progress in the last
40 years has increased the containment time to Δt≅1000r
2/D
B.
One existing fusion reactor concept is the Tokamak. The magnetic field of a Tokamak
68 and a typical particle orbit 66 are illustrated in FIG. 5.
For the past 30 years, fusion efforts have been focussed on the Tokamak reactor
using a D-T fuel. These efforts have culminated in the International Thermonuclear
Experimental Reactor (ITER), illustrated in FIG. 7. Recent experiments with
Tokamaks suggest that classical transport, Δt≅r
2/D
c,
is possible, in which case the minimum plasma dimension can be reduced from meters
to centimeters. These experiments involved the injection of energetic beams (50
to 100 keV), to heat the plasma to temperatures of 10 to 30 keV. See W. Heidbrink
& G. J. Sadler, 34
Nuclear Fusion 535 (1994). The energetic beam ions in
these experiments were observed to slow down and diffuse classically while the
thermal plasma continued to diffuse anomalously fast. The reason for this is that
the energetic beam ions have a large gyroradius and, as such, are insensitive to
fluctuations with wavelengths shorter than the ion gyroradius (λ<α
i).
The short-wavelength fluctuations tend to average over a cycle and thus cancel.
Electrons, however, have a much smaller gyroradius, so they respond to the fluctuations
and transport anomalously.
Because of anomalous transport, the minimum dimension of the plasma must
be at least 2.8 meters. Due to this dimension, the ITER was created 30 meters high
and 30 meters in diameter. This is the smallest D-T Tokamak-type reactor that is
feasible. For advanced fuels, such as D-He
3 and p-B
11, the
Tokamak-type reactor would have to be much larger because the time for a fuel ion
to have a nuclear reaction is much longer. A Tokamak reactor using D-T fuel has
the additional problem that most of the energy of the fusion products energy is
carried by 14 MeV neutrons, which cause radiation damage and induce reactivity
in almost all construction materials due to the neutron flux. In addition, the
conversion of their energy into electricity must be by a thermal process, which
is not more than 30% efficient.
Another proposed reactor configuration is a colliding beam reactor. In a
colliding beam reactor, a background plasma is bombarded by beams of ions. The
beams comprise ions with an energy that is much larger than the thermal plasma.
Producing useful fusion reactions in this type of reactor has been infeasible because
the background plasma slows down the ion beams. Various proposals have been made
to reduce this problem and maximize the number of nuclear reactions.
For example, U.S. Pat. No. 4,065,351 to Jassby et al. discloses a method of producing
counterstreaming colliding beams of deuterons and tritons in a toroidal confinement
system. In U.S. Pat. No. 4,057,462 to Jassby et al., electromagnetic energy is
injected to counteract the effects of bulk equilibrium plasma drag on one of the
ion species. The toroidal confinement system is identified as a Tokamak. In U.S.
Pat. No. 4,894,199 to Rostoker, beams of deuterium and tritium are injected and
trapped with the same average velocity in a Tokamak, mirror, or field reversed
configuration. There is a low density cool background plasma for the sole purpose
of trapping the beams. The beams react because they have a high temperature, and
slowing down is mainly caused by electrons that accompany the injected ions. The
electrons are heated by the ions in which case the slowing down is minimal.
In none of these devices, however, does an equilibrium electric field play any
part. Further, there is no attempt to reduce, or even consider, anomalous transport.
Other patents consider electrostatic confinement of ions and, in some cases,
magnetic confinement of electrons. These include U.S. Pat. No. 3,258,402 to Farnsworth
and U.S. Pat. No. 3,386,883 to Farnsworth, which disclose electrostatic confinement
of ions and inertial confinement of electrons; U.S. Pat. No. 3,530,036 to Hirsch
et al. and U.S. Pat. No. 3,530,497 to Hirsch et al. are similar to Farnsworth;
U.S. Pat. No. 4,233,537 to Limpaecher, which discloses electrostatic confinement
of ions and magnetic confinement of electrons with multipole cusp reflecting walls;
and U.S. Pat. No. 4,826,646 to Bussard, which is similar to Limpaecher and involves
point cusps. None of these patents consider electrostatic confinement of electrons
and magnetic confinement of ions. Although there have been many research projects
on electrostatic confinement of ions, none of them have succeeded in establishing
the required electrostatic fields when the ions have the required density for a
fusion reactor. Lastly, none of the patents cited above discuss a field reversed
configuration magnetic topology.
The field reversed configuration (FRC) was discovered accidentally around 1960
at the Naval Research Laboratory during theta pinch experiments. A typical FRC
topology, wherein the internal magnetic field reverses direction, is illustrated
in FIG. 8 and FIG. 10, and particle orbits in a FRC are shown in FIG. 11
and FIG. 14. Regarding the FRC, many research programs have been supported
in the United States and Japan. There is a comprehensive review paper on the theory
and experiments of FRC research from 1960-1988. See M. Tuszewski, 28
Nuclear
Fusion 2033, (1988). A white paper on FRC development describes the research
in 1996 and recommendations for future research. See L. C. Steinhauer et al., 30
Fusion Technology 116 (1996). To this date, in FRC experiments the FRC has
been formed with the theta pinch method. A consequence of this formation method
is that the ions and electrons each carry half the current, which results in a
negligible electrostatic field in the plasma and no electrostatic confinement.
The ions and electrons in these FRCs were contained magnetically. In almost all
FRC experiments, anomalous transport has been assumed. See, e.g., Tuszewski, beginning
of section 1.5.2, at page 2072.
SUMMARY OF THE INVENTION
To address the problems faced by previous plasma containment systems, a system
and apparatus for containing plasma are herein described in which plasma ions are
contained magnetically in stable, large orbits and electrons are contained electrostatically
in an energy well. A major innovation of the present invention over all previous
work with FRCs is the simultaneous electrostatic confinement of electrons and magnetic
confinement of ions, which tends to avoid anomalous transport and facilitate classical
containment of both electrons and ions. In this configuration, ions may have adequate
density and temperature so that upon collisions they are fused together by the
nuclear force, thus releasing fusion energy.
In a preferred embodiment, a plasma confinement system comprises a chamber, a
magnetic field generator for applying a magnetic field in a direction substantially
along a principle axis, and an annular plasma layer that comprises a circulating
beam of ions. Ions of the annular plasma beam layer are substantially contained
within the chamber magnetically in orbits and the electrons are substantially contained
in an electrostatic energy well. In one aspect of one preferred embodiment a magnetic
field generator comprises a current coil. Preferably, the system further comprises
mirror coils near the ends of the chamber that increase the magnitude of the applied
magnetic field at the ends of the chamber. The system may also comprise a beam
injector for injecting a neutralized ion beam into the applied magnetic field,
wherein the beam enters an orbit due to the force caused by the applied magnetic
field. In another aspect of the preferred embodiments, the system forms a magnetic
field having a topology of a field reversed configuration.
Also disclosed is a method of confining plasma comprising the steps of magnetically
confining the ions in orbits within a magnetic field and electrostatically confining
the electrons in an energy well. An applied magnetic field may be tuned to produce
and control the electrostatic field. In one aspect of the method the field is tuned
so that the average electron velocity is approximately zero. In another aspect,
the field is tuned so that the average electron velocity is in the same direction
as the average ion velocity. In another aspect of the method, the method forms
a field reversed configuration magnetic field, in which the plasma is confined.
In another aspect of the preferred embodiments, an annular plasma layer is contained
within a field reversed configuration magnetic field. The plasma layer comprises
positively charged ions, wherein substantially all of the ions are non-adiabatic,
and electrons contained within an electrostatic energy well. The plasma layer is
caused to rotate and form a magnetic self-field of sufficient magnitude to cause
field reversal.
In other aspects of the preferred embodiments, the plasma may comprise at least
two different ion species, one or both of which may comprise advanced fuels.
Having a non-adiabatic plasma of energetic, large-orbit ions tends to prevent
the anomalous transport of ions. This can be done in a FRC, because the magnetic
field vanishes (i.e., is zero) over a surface within the plasma. Ions having a
large orbit tend to be insensitive to short-wavelength fluctuations that cause
anomalous transport.
Magnetic confinement is ineffective for electrons because they have a small
gyroradius—due to their small mass—and are therefore sensitive to
short-wavelength fluctuations that cause anomalous transport. Therefore, the electrons
are effectively confined in a deep potential well by an electrostatic field, which
tends to prevent the anomalous transport of energy by electrons. The electrons
that escape confinement must travel from the high density region near the null
surface to the surface of the plasma. In so doing, most of their energy is spent
in ascending the energy well. When electrons reach the plasma surface and leave
with fusion product ions, they have little energy left to transport. The strong
electrostatic field also tends to make all the ion drift orbits rotate in the diamagnetic
direction, so that they are contained. The electrostatic field further provides
a cooling mechanism for electrons, which reduces their radiation losses.
The increased containment ability allows for the use of advanced fuels such as
D-He
3 and p-B
11, as well as neutronic reactants such as D-D
and D-T. In the D-He
3 reaction, fast neutrons are produced by secondary
reactions, but are an improvement over the D-T reaction. The p-B
11 reaction,
and the like, is preferable because it avoids the problems of fast neutrons completely.
Another advantage of the advanced fuels is the direct energy conversion of
energy from the fusion reaction because the fusion products are moving charged
particles, which create an electrical current. This is a significant improvement
over Tokamaks, for example, where a thermal conversion process is used to convert
the kinetic energy of fast neutrons into electricity. The efficiency of a thermal
conversion process is lower than 30%, whereas the efficiency of direct energy conversion
can be as high as 90%.
Other aspects and features of the present invention will become apparent from
consideration of the following description taken in conjunction with the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
Preferred embodiments are illustrated by way of example, and not by way
of limitation, in the figures of the accompanying drawings, in which like reference
numerals refer to like components.
FIGS. 1A and 1B show, respectively, the Lorentz force acting on a positive
and a negative charge.
FIGS. 2A and 2B show Larmor orbits of charged particles in a constant magnetic field.
FIG. 3 shows the {right arrow over (E)}×{right arrow over (B)} drift.
FIG. 4 shows the gradient drift.
FIG. 5 shows an adiabatic particle orbit in a Tokamak.
FIG. 6 shows a non-adiabatic particle orbit in a betatron.
FIG. 7 shows the International Thermonuclear Experimental Reactor (ITER).
FIG. 8 shows the magnetic field of a FRC.
FIGS. 9A and 9B show, respectively, the diamagnetic and the counterdiamagnetic
direction in a FRC.
FIG. 10 shows the colliding beam system.
FIG. 11 shows a betatron orbit.
FIGS. 12A and 12B show, respectively, the magnetic field and the direction
of the gradient drift in a FRC.
FIGS. 13A and 13B show, respectively, the electric field and the direction
of the {fraction (E)}×{fraction (B)} drift in a FRC.
FIGS. 14A, 14B and 14C show ion drift orbits.
FIGS. 15A and 15B show the Lorentz force at the ends of a FRC.
FIGS. 16A and 16B show the tuning of the electric field and the electric potential
in the colliding beam system.
FIG. 17 shows a Maxwell distribution.
FIGS. 18A and 18B show transitions from betatron orbits to drift orbits due
to large-angle, ion-ion collisions.
FIG. 19 show A, B, C and D betatron orbits when small-angle, electron-ion collisions
are considered.
FIGS. 20A, 20B and 20C show the reversal of the magnetic field
in a FRC.
FIGS. 21A, 21B, 21C and 21D show the effects due to tuning
of the external magnetic field B
0 in a FRC.
FIGS. 22A, 22B, 22C and 22D show iteration results for
a D-T plasma.
FIGS. 23A, 23B, 23C, and 23D show iteration results for
a D-He
3 plasma.
FIG. 24 shows iteration results for a p-B
11 plasma.
FIG. 25 shows an exemplary confinement chamber.
FIG. 26 shows a neutralized ion beam as it is electrically polarized before
entering a confining chamber.
FIG. 27 is a head-on view of a neutralized ion beam as it contacts plasma in
a confining chamber.
FIG. 28 is a side view schematic of a confining chamber according to a preferred
embodiment of a start-up procedure.
FIG. 29 is a side view schematic of a confining chamber according to another
preferred embodiment of a start-up procedure.
FIG. 30 shows traces of B-dot probe indicating the formation of a FRC.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
An ideal fusion reactor solves the problem of anomalous transport for both ions
and electrons. The anomalous transport of ions is avoided by magnetic confinement
in a field reversed configuration (FRC) in such a way that the majority of the
ions have large, non-adiabatic orbits, making them insensitive to short-wavelength
fluctuations that cause anomalous transport of adiabatic ions. For electrons, the
anomalous transport of energy is avoided by tuning the externally applied magnetic
field to develop a strong electric field, which confines them electrostatically
in a deep potential well. Moreover, the fusion fuel plasmas that can be used with
the present confinement process and apparatus are not limited to neutronic fuels
only, but also advantageously include advanced fuels. (For a discussion of advanced
fuels, see R. Feldbacher & M. Heindler,
Nuclear Instruments and Methods in Physics
Research, A271(1988)JJ-64 (North Holland Amsterdam).)
The solution to the problem of anomalous transport found herein makes use of
a specific magnetic field configuration, which is the FRC. In particular, the existence
of a region in a FRC where the magnetic field vanishes makes it possible to have
a plasma comprising a majority of non-adiabatic ions.
Background Theory
Before describing the system and apparatus in detail, it will be helpful to
first review a few key concepts necessary to understand the concepts contained herein.
Lorentz Force and Particle Orbits in a Magnetic Field
A particle with electric charge q moving with velocity {right arrow over (ν)}
in a magnetic field {right arrow over (B)} experiences a force {right arrow over
(F)}
L given by
##EQU1##
The force {right arrow over (F)}
L is called the Lorentz force. It,
as well as all the formulas used in the present discussion, is given in the gaussian
system of units. The direction of the Lorentz force depends on the sign of the
electric charge q. The force is perpendicular to both velocity and magnetic field.
FIG. 1A shows the Lorentz force
30 acting on a positive charge. The velocity
of the particle is shown by the vector
32. The magnetic field is
34.
Similarly, FIG. 1B shows the Lorentz force
30 acting on a negative charge.
As explained, the Lorentz force is perpendicular to the velocity of a particle;
thus, a magnetic field is unable to exert force in the direction of the particle's
velocity. It follows from Newton's second law, {right arrow over (F)}=m{right arrow
over (a)}, that a magnetic field is unable to accelerate a particle in the direction
of its velocity. A magnetic field can only bend the orbit of a particle, but the
magnitude of its velocity is not affected by a magnetic field.
FIG. 2A shows the orbit of a positively charged particle in a constant magnetic
field
34. The Lorentz force
30 in this case is constant in magnitude,
and the orbit
36 of the particle forms a circle. This circular orbit
36
is called a Larmor orbit. The radius of the circular orbit
36 is called
a gyroradius
38.
Usually, the velocity of a particle has a component that is parallel to
the magnetic field and a component that is perpendicular to the field. In such
a case, the particle undergoes two simultaneous motions: a rotation around the
magnetic field line and a translation along it. The combination of these two motions
creates a helix that follows the magnetic field line
40. This is indicated
in FIG.
2B.
A particle in its Larmor orbit revolves around a magnetic field line. The number
of radians traveled per unit time is the particle's gyrofrequency, which is denoted
by Ω and given by
##EQU2##
where m is the mass of the particle and c is the speed of light. The gyroradius
α
L of a charged particle is given by
##EQU3##
where ν
⊥ is the component of the velocity of the particle
perpendicular to the magnetic field.
{right arrow over (E)}×{right arrow over (B)} Drift and Gradient Drift
Electric fields affect the orbits of charged particles, as shown in FIG.
3. In FIG. 3, the magnetic field
44 points toward the reader. The
orbit of a positively charged ion due to the magnetic field
44 alone would
be a circle
36; the same is true for an electron
42. In the presence
of an electric field
46, however, when the ion moves in the direction of
the electric field
46, its velocity increases. As can be appreciated, the
ion is accelerated by the force q{right arrow over (E)}. It can further be seen
that, according to Eq. 3, the ion's gyroradius will increase as its velocity does.
As the ion is accelerated by the electric field
46, the magnetic field
44 bends the ion's orbit. At a certain point the ion reverses direction
and begins to move in a direction opposite to the electric field
46. When
this happens, the ion is decelerated, and its gyroradius therefore decreases. The
ion's gyroradius thus increases and decreases in alternation, which gives rise
to a sideways drift of the ion orbit
48 in the direction
50 as shown
in FIG.
3. This motion is called {right arrow over (E)}×{right arrow
over (B)} drift. Similarly, electron orbits
52 drift in the same direction
50.
A similar drift can be caused by a gradient of the magnetic field
44 as
illustrated in FIG.
4. In FIG. 4, the magnetic field
44 points towards
the reader. The gradient of the magnetic field is in the direction
56. The
increase of the magnetic field's strength is depicted by the denser amount of dots
in the figure.
From Eqs. 2 and 3, it follows that the gyroradius is inversely proportional
to the strength of the magnetic field. When an ion moves in the direction of increasing
magnetic field its gyroradius will decrease, because the Lorentz force increases,
and vice versa. The ion's gyroradius thus decreases and increases in alternation,
which gives rise to a sideways drift of the ion orbit
58 in the direction
60. This motion is called gradient drift. Electron orbits
62 drift
in the opposite direction
64.
Adiabatic and Non-Adiabatic Particles
Most plasma comprises adiabatic particles. An adiabatic particle tightly follows
the magnetic field lines and has a small gyroradius. FIG. 5 shows a particle orbit
66 of an adiabatic particle that follows tightly a magnetic field line
68.
The magnetic field lines
68 depicted are those of a Tokamak.
A non-adiabatic particle has a large gyroradius. It does not follow the magnetic
field lines and is usually energetic. There exist other plasmas that comprise non-adiabatic
particles. FIG. 6 illustrates a non-adiabatic plasma for the case of a betatron.
The pole pieces
70 generate a magnetic field
72. As FIG. 6 illustrates,
the particle orbits
74 do not follow the magnetic field lines
72.
Radiation in Plasmas
A moving charged particle radiates electromagnetic waves. The power radiated
by
the particle is proportional to the square of the charge. The charge of an ion
is Ze, where e is the electron charge and Z is the atomic number. Therefore, for
each ion there will be Z free electrons that will radiate. The total power radiated
by these Z electrons is proportional to the cube of the atomic number (Z
3).
Charged Particles in a FRC
FIG. 8 shows the magnetic field of a FRC. The system has cylindrical symmetry
with respect to its axis
78. In the FRC, there are two regions of magnetic
field lines: open
80 and closed
82. The surface dividing the two
regions is called the separatrix
84. The FRC forms a cylindrical null surface
86 in which the magnetic field vanishes. In the central part
88 of
the FRC the magnetic field does not change appreciably in the axial direction.
At the ends
90, the magnetic field does change appreciably in the axial
direction. The magnetic field along the center axis
78 reverses direction
in the FRC, which gives rise to the term "Reversed" in Field Reversed Configuration (FRC).
In FIG. 9A, the magnetic field outside of the null surface
94 is in the
direction
96. The magnetic field inside the null surface is in the direction
98. If an ion moves in the direction
100, the Lorentz force
30
acting on it points towards the null surface
94. This is easily appreciated
by applying the right-hand rule. For particles moving in the direction
102,
called diamagnetic, the Lorentz force always points toward the null surface
94.
This phenomenon gives rise to a particle orbit called betatron orbit, to be described below.
FIG. 9B shows an ion moving in the direction
104, called counterdiamagnetic.
The Lorentz force in this case points away from the null surface
94. This
phenomenon gives rise to a type of orbit called a drift orbit, to be described
below. The diamagnetic direction for ions is counterdiamagnetic for electrons,
and vice versa.
FIG. 10 shows a ring or annular layer of plasma
106 rotating in the ions'
diamagnetic direction
102. The ring
106 is located around the null
surface
86. The magnetic field
108 created by the annular plasma
layer
106, in combination with an externally applied magnetic field
110,
forms a magnetic field having the topology of a FRC (The topology is shown in FIG.
8).
The ion beam that forms the plasma layer
106 has a temperature; therefore,
the velocities of the ions form a Maxwell distribution in a frame rotating at the
average angular velocity of the ion beam. Collisions between ions of different
velocities lead to fusion reactions. For this reason, the plasma beam layer
106
is called a colliding beam system.
FIG. 11 shows the main type of ion orbits in a colliding beam system, called
a betatron orbit
112. A betatron orbit
112 can be expressed as a
sine wave centered on the null circle
114. As explained above, the magnetic
field on the null circle
114 vanishes. The plane of the orbit
112
is perpendicular to the axis
78 of the FRC. Ions in this orbit
112
move in their diamagnetic direction
102 from a starting point
116.
An ion in a betatron orbit has two motions: an oscillation in the radial direction
(perpendicular to the null circle
114), and a translation along the null
circle
114.
FIG. 12A is a graph of the magnetic field
118 in a FRC. The field
118
is derived using a one-dimensional equilibrium model, to be discussed below in
conjunction with the theory of the invention. The horizontal axis of the graph
represents the distance in centimeters from the FRC axis
78. The magnetic
field is in kilogauss. As the graph depicts, the magnetic field
118 vanishes
at the null circle radius
120.
As shown in FIG. 12B, a particle moving near the null circle will see a gradient
126 of the magnetic field pointing away from the null surface
86.
The magnetic field outside the null circle is
122, while the magnetic field
inside the null circle is
124. The direction of the gradient drift is given
by the cross product {right arrow over (B)}×∇B, where ∇B is
the gradient of the magnetic field; thus, it can be appreciated by applying the
right-hand rule that the direction of the gradient drift is in the counterdiamagnetic
direction, whether the ion is outside or inside the null circle
128.
FIG. 13A is a graph of the electric field
130 in a FRC. The field
130
is derived using a one-dimensional equilibrium model, to be discussed below in
conjunction with the theory of the invention. The horizontal axis of the graph
represents the distance in centimeters from the FRC axis
78. The electric
field is in volts/cm. As the graph depicts, the electric field
130 vanishes
close to the null circle radius
120.
As shown if FIG. 13B, the electric field for ions is deconfining; it points away
from the null surface
132,
134. The magnetic field, as before, is
in the directions
122,
124. It can be appreciated by applying the
right-hand rule that the direction of the {right arrow over (E)}×{right arrow
over (B)} drift is in the diamagnetic direction, whether the ion is outside or
inside the null surface
136.
FIGS. 14A and 14B show another type of common orbit in a FRC, called a drift
orbit
138. Drift orbits
138 can be outside of the null surface, as
shown in FIG. 14A, or inside it, as shown in FIG.
14B. Drift orbits
138
rotate in the diamagnetic direction if the {right arrow over (E)}×{right arrow
over (B)} drift dominates or in the counterdiamagnetic direction if the gradient
drift dominates. The drift orbits
138 shown in FIGS. 14A and 14B rotate
in the diamagnetic direction
102 from starting point
116.
A drift orbit, as shown in FIG. 14C, can be thought of as a small circle rolling
over a relatively bigger circle. The small circle
142 spins around its axis
in the sense
144. It also rolls over the big circle
146 in the direction
102. The point
140 will trace in space a path similar to
138.
FIGS. 15A and 15B show the direction of the Lorentz force at the ends of a
FRC. In FIG. 15A, an ion is shown moving in the diamagnetic direction
102
with a velocity
148 in a magnetic field
150. It can be appreciated
by applying the right-hand rule that the Lorentz force
152 tends to push
the ion back into the region of closed field lines. In this case, therefore, the
Lorentz force
152 is confining for the ions. In FIG. 15B, an ion is shown
moving in the counterdiamagnetic direction with a velocity
148 in a magnetic
field
150. It can be appreciated by applying the right-hand rule that the
Lorentz force
152 tends to push the ion into the region of open field lines.
In this case, therefore, the Lorentz force
152 is deconfining for the ions.
Magnetic and Electrostatic Confinement in a FRC
A plasma layer
106 (see FIG. 10) can be formed in a FRC by injecting energetic
ion be
