Self-generation of magnetic fields
The stars generate self-magnetic fields on large spatial scales and long time scales, and laser-produced plasmas generate intense self-magnetic fields on very short spatial and time scales. Two questions are posed: (1) Could a self-magnetic field be generated in a laboratory plasma with intermediate...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2000
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| Цитувати: | Self-generation of magnetic fields / T.J. Dolan // Вопросы атомной науки и техники. — 2000. — № 3. — С. 78-80. — Бібліогр.: 9 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859668847719612416 |
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| author | Dolan, T.J. |
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| citation_txt | Self-generation of magnetic fields / T.J. Dolan // Вопросы атомной науки и техники. — 2000. — № 3. — С. 78-80. — Бібліогр.: 9 назв. — англ. |
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| container_title | Вопросы атомной науки и техники |
| description | The stars generate self-magnetic fields on large spatial scales and long time scales, and laser-produced plasmas generate intense self-magnetic fields on very short spatial and time scales. Two questions are posed: (1) Could a self-magnetic field be generated in a laboratory plasma with intermediate spatial and time scales? (2) If a self-magnetic field were generated, would it evolve towards a minimum energy state? If the answers turned out to be affirmative, then self-magnetic fields could possibly have interesting applications.
|
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UDC 533.9
Problems of Atomic Science and Technology. 2000. N 3. Series: Plasma Physics (5). p. 78-80 78
SELF-GENERATION OF MAGNETIC FIELDS
Thomas J. Dolan, International Atomic Energy Agency
The stars generate self-magnetic fields on large spatial scales and long time scales, and laser-produced
plasmas generate intense self-magnetic fields on very short spatial and time scales. Two questions are posed: (1)
Could a self-magnetic field be generated in a laboratory plasma with intermediate spatial and time scales? (2) If a
self-magnetic field were generated, would it evolve towards a minimum energy state? If the answers turned out to
be affirmative, then self-magnetic fields could possibly have interesting applications.
INTRODUCTION
Self-generation of magnetic fields is not
unusual in conducting fluids. The earth generates its
own magnetic field from a dynamo effect in a weakly
conducting fluid. The sun generates its own magnetic
field on large spatial scales and time scales from a
dynamo effect. A laboratory plasma with n = 1018 m-3
and Te = 100 eV would be intermediate between the sun
and a laser-produced plasma, which generate self-
magnetic fields (Table 1).
Could a significant self-magnetic field be
induced by high-power electromagnetic wave
input into a laboratory plasma?
SELF-MAGNETIC FIELD GENERATION
MECHANISMS
The growth rate of magnetic induction can be
estimated from a combination of Faraday's Law and a
generalized Ohm's law as
∂B/∂t = ∇∇ × u × B - ∇∇ × (J × B/ne)
+ (1/en) ∇∇Te × ∇∇n - ∇∇ × (RT/en)
- ∇∇ × (ηparJpar + ηperpJperp),
(1)
where
RT = -0.71 n ∇∇ parTe - 1.5(n/Ωeτe) b × ∇∇Te (2)
is the thermal force, u = flow velocity, J = plasma
current density, n = electron density, Te = electron
temperature (J), e = electronic charge, η = plasma
resistivity, Ωe = electron gyrofrequency, τe = electron
collision time, b = unit vector parallel to B, and par
and perp refer to vector components parallel and
perpendicular to B. [from Sudan,1 changed into SI
units]. The third and fourth terms on the right hand side
of Eq.(1) can be sources for a self-generated magnetic
field. Thus, a self-magnetic field tends to be generated
when the density and temperature gradients are not
parallel or when there is a nonzero curl of the thermal
force.
If the directions of the density and temperature
gradients differ by an angle α, then the density gradient
source term
(∂B/∂t ) ∇∇ n = (1/en)∇∇Te × ∇∇n ≈ sin(α) Te/e Ln LT , (3)
where Ln , LT = characteristic gradient scale lengths of
density and temperature. In a laser-produced plasma
with Te/e ≈ 100 eV and Ln ≈ LT ≈ 10 microns, if α ≈ 3
degrees, then the density-gradient source term would
be
about 50 T/ns. Self-magnetic fields on the order of
100 T have been observed in laser-plasma interaction
experiments.
Table 1. Approximate parameters of sun,
laboratory plasma, and laser-produced plasma.
Units
Sun,
corona
Laboratory
plasma
Laser-
produced
plasma
n
m-3 1013 1018 1027
T
eV 100 100 1000
R
m 108 1 10-4
Time
scale
s 103 1 10-9
B T 10-9 up to
0.3
(sunspots)
? > 100
There are at least five mechanisms by which
self-magnetic fields can be generated:
1. Density gradient term, Eq. (1)
2. Curl of the thermal force, Eq. (1)
3. Ponderomotive force. The Ponderomotive effect
occurs at very high power fluxes and is not likely to
play a significant role in the laboratory plasma of
Table1.
4. Inverse Faraday effect. Horowitz and coworkers
irradiated plasma inside a spherical metal shell with an
intense circularly polarized laser beam. In experiments
with 1.06 µm laser light at irradiances of 109 - 1014
W/cm2, they measured axial magnetic fields from 0.05
-- 200 T.2 An axial magnetic field was generated from
circularly polarized light via an inverse Faraday effect
and a toroidal magnetic field by the density gradient
term. These experiments suggest that, by controlling
the polarization of the incident electromagnetic
79
radiation, one can stimulate various magnetic field
components in the plasma.
5. Self-organization driven by turbulence. The total
magnetic viscosity = η + ηturb. The kinematic magnetic
viscosity η is always positive, but the turbulent
magnetic viscosity ηturb becomes negative if the
magnetic energy of small-scale turbulence exceeds the
kinetic energy. A negative magnetic viscosity effect
can lead to the appearance of a large-scale magnetic
field growing from small-scale perturbations.
Chechkin studied the phenomenon of a long-
wavelength instability in a system of small-scale flows
or vortices, with the energy of the small-scale
turbulence being sustained by external means. When
the small-scale magnetic field perturbation amplitude
exceeds a critical value, a large-scale magnetic field
can grow. This growth is analogous to the negative
viscosity effect of the Kolmogorov flow instability in
ordinary fluids. The negative magnetic viscosity effect
can lead to amplification of the large-scale field and is
a possible mechanism for explaining explosive
magnetic phenomena in solar flares and tokamak
disruptions. 3 4
Of the five mechanisms for generation of self-
magnetic fields, the density gradient term and the self-
organization driven by turbulence appear to be the most
likely to be effective in the laboratory plasma of Table
1. Let us consider how these mechanisms might be
induced.
plasma
source
Te
ne
z
Figure 1. Axial density gradient due to non-uniform
plasma source.
DENSITY GRADIENT TERM
Consider a long cylindrical plasma with a weak
axial magnetic field, Figure 1. Rapid electron motion
along magnetic field lines would tend to keep the
electron temperature uniform in the z direction, so the
electron temperature gradient would be essentially in
the radial direction. The density gradient source term
(1/en)∇∇Te × ∇∇n could be significant only if a
substantial non-radial component of the density
gradient could be produced. For example, a plasma
density source at one axial location could cause an
axial component of the density gradient. Assuming
diffusive loss radially and axial flow at the ion sound
speed uz ~ [(Te+Ti)/M]1/2, the resulting density gradient
term was estimated to be 5
∂Bθ/∂t ~ (1/ne)(∂Te/∂r)(∂n/∂z) ~ (DTe/ea2 uz). (4)
For a plasma with D ~ 300 m2/s, Te/e ~ 10 eV, a ~ 0.3
m, and uz ~ 3x104 m/s, the density gradient term would
be ∂Bθ/∂t ~ 1 T/s. Thus, a density gradient term could
be induced by a non-uniform plasma source in this
simplified model. The induced magnetic field,
however, would also change the plasma behavior. A
multidimensional, multifluid model, including
momentum and energy conservation, collisions,
turbulence, magnetic reconnection, wave-particle
interactions, and wall interactions would be needed to
derive an accurate description of these complex
phenomena.
TURBULENCE
Very high power fluxes of electromagnetic
waves might be required for brief periods of time in
order to induce a high degree of turbulence that could
trigger the negative magnetic viscosity phenomenon.
The required power flux remains to be estimated as a
function of plasma parameters. A lower bound is the
input power required to sustain the plasma against
radiation losses from heat conduction, bremsstrahlung
and line radiation. It was estimated7 that a plasma with
a ~ 0.3 m, n = 1018 m-3, Te = 100 eV, 5 % carbon
impurity, and initial bias field B ~ 0.01 T would have a
power loss rate about 0.4 MW/m3. Input power fluxes
up to about 10 MW/m2. have been injected into
tokamak plasmas. Higher fluxes are conceivable for
short periods of time. There are power flux limitations
due to window damage and arcing of waveguides or
antennas. The required input power might be reduced if
the magnetic field start-up region could be restricted
to a small plasma volume, and then allowed to expand
after the self-magnetic field got started.
If a self-magnetic field were generated, would
it evolve towards a minimum energy state?
SELF-ORGNIZATION
Self-organization phenomena are observed in
many areas of nature, such as Benard convection cells,
snowflakes, autocatalytic chemical reactions, amoeba
life cycles, materials science, electrical circuits,
lasers, climate changes, entomology, and human
society. 6 Therefore, it is natural to speculate that
self-organization might occur in a plasma with regard
to magnetic field generation and evolution towards a
minimum energy state.
Under some circumstances plasmas tend to evolve
towards a minimum energy state described by the
equation ∇∇ × B = λ B, where B = magnetic
induction and λ is the "Taylor parameter", which would
80
be spatially uniform in an ideal minimum-energy
configuration. Spheromak plasmas, which tend to
approximate this minimum energy state, have been
generated by flux cores, by combined theta-Z pinches,
by coaxial plasma guns, by conical theta pinches, by
kinked Z pinches, and by electrostatic helicity
injection. In view of their natural stability, it may be
feasible to compress spheromak plasmas, and
spheromak plasmoids have been injected across
magnetic field lines into a tokamak. Often a "dynamo"
involving magnetic reconnection adjusts the magnetic
field towards the minimum energy state. Usually the
plasma resistivity is high in the cool edge region, so
the current density and λ are low at the edge. The
minimum-energy state (uniform λ profile) is not fully
achieved (the configuration is "nearly-minimum-
energy"), and the gradient of λ drives turbulence that
tends to move the plasma towards the minimum energy
state.7
Various plasma self-organization phenomena
have been observed experimentally. Plasma filaments
formed by microwave discharges at high pressures tend
to evolve towards "attractors." Whistler waves induced
in low-density plasmas tend to evolve towards
magnetic field configurations resembling three-
dimensional Hill's vortices, sometimes forming
knotted flux tubes. If excess plasma energy generated
by magnetic reconnection is not removed, then a force-
balanced equilibrium (∇∇p = JxB) may result, rather
than a Taylor minimum-energy state.8 Thermal
conduction would tend to reduce the pressure gradient
and perpendicular current, aiding the approach to a
minimum-energy state. 9
________________________________________
flux conserver insulator conducting wall
Figure 2. Compact toroid sustained inside flux
conserver.
DISCUSSION
The questions of self-magnetic field generation
and of possible evolution to a minimum energy state
have been raised for consideration. If a self-magnetic
field were generated and tended towards a minimum
energy state, then it would be of interest to try to
sustain the minimum energy plasmoid configuration
while increasing the plasma density and temperature. A
metal first wall could help damp high-frequency
disturbances, and a superconducting flux conserver
outside the chamber could help stabilize the plasma on
longer time scales. Such a self-generated plasma
configuration could possibly reduce the need for
external high-field magnets and structural supports.
To study these issues a three-dimensional
computer simulation including estimates of the
optimum wave frequencies, polarizations, and possible
cavity modes, could be helpful. Various experimental
tests can be envisioned. For example, an extremely
high flux of electromagnetic waves could be injected
into a toroidal metal chamber surrounded by a high
temperature superconducting (HTSC) flux conserver,
as illustrated in Figure 2, with a non-uniform plasma
source. If needed, a magnet coil inside the HTSC shell
could provide a weak bias field to enhance start-up.
REFERENCES
1 R. N. SUDAN, "Generation of ultra-high magnetic
fields by high power lasers," Laser Interaction and
Related Plasma Phenomena, AIP Conference
Proceedings 318, American Institute of Physics
(1994), p. 91-96.
2 Y. HOROWITZ, S. ELIEZER, Z. HENIS, Y. PAISS, E.
MOSHE, A. LUDMIRSKY, M. WERDIGER, B. ARAD,
A. ZIGLER, "The inverse Faraday effect in plasmas
produced by circularly polarized laser light in the range
of intensities 109 - 1014 W/cm2," Phys. Lett. A, 246,
329-334 (1998).
3 A. V. CHECHKIN, “Generation of magnetic fields in
a 2D magnetic fluid in the presence of small-scale
spatial-periodic perturbations,” Ukrainian Journal of
Physics 44, No.6 (1999) 712-717.
4 A. V. CHECHKIN, “Negative magnetic viscosity in
two dimensions,” Journal of Experimental and
Theoretical Physics 89, 677-688 (1999).
5 T. J. DOLAN, “Possible generation of self-magnetic
fields,” manuscript in preparation. (available from the
author)
6 G. NICOLIS and I. PRIGOGINE, Exploring
Complexity, W. H. Freeman & Company, New York,
1989.
7 P. M. BELLAN, Spheromaks, Imperial College
Press, London, 2000.
8 T. SATO and the COMPLEXITY SIMULATION
GROUP, “Complexity in plasma: From self-
organization to geodynamo,” Physics of Plasmas 3,
2135-2142 (1996).
9 S.-P. ZHU, R. HORIUCHI, T. SATO, and the
COMPLEXITY SIMULATION GROUP, “Self-
organization process of a magnetohydrodynamic
plasma in the presence of thermal conduction,”
Physics of Plasmas 3, 2821-2823 (1996).
|
| id | nasplib_isofts_kiev_ua-123456789-82392 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-11-30T12:37:45Z |
| publishDate | 2000 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Dolan, T.J. 2015-05-29T08:24:16Z 2015-05-29T08:24:16Z 2000 Self-generation of magnetic fields / T.J. Dolan // Вопросы атомной науки и техники. — 2000. — № 3. — С. 78-80. — Бібліогр.: 9 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/82392 533.9 The stars generate self-magnetic fields on large spatial scales and long time scales, and laser-produced plasmas generate intense self-magnetic fields on very short spatial and time scales. Two questions are posed: (1) Could a self-magnetic field be generated in a laboratory plasma with intermediate spatial and time scales? (2) If a self-magnetic field were generated, would it evolve towards a minimum energy state? If the answers turned out to be affirmative, then self-magnetic fields could possibly have interesting applications. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Рlasma Dynamics and Plasma-Wall Interaction Self-generation of magnetic fields Article published earlier |
| spellingShingle | Self-generation of magnetic fields Dolan, T.J. Рlasma Dynamics and Plasma-Wall Interaction |
| title | Self-generation of magnetic fields |
| title_full | Self-generation of magnetic fields |
| title_fullStr | Self-generation of magnetic fields |
| title_full_unstemmed | Self-generation of magnetic fields |
| title_short | Self-generation of magnetic fields |
| title_sort | self-generation of magnetic fields |
| topic | Рlasma Dynamics and Plasma-Wall Interaction |
| topic_facet | Рlasma Dynamics and Plasma-Wall Interaction |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/82392 |
| work_keys_str_mv | AT dolantj selfgenerationofmagneticfields |