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Parallel
Computations in Plasma Diagnostics
Effect of Plasma Environment on Charge
Exchange
We collaborate with the group of
Prof. Oks at Auburn University in studying the effect of the plasma environment
on charge exchange in magnetic fusion plasmas. A practical purpose of
classical calculations is two-fold. First, they should stimulate more
quantal simulations of this effect (though the quantal simulations are
computationally-expensive). Second, for diagnostics, whose input requires
computing simultaneously hundreds of different cross-sections of charge
exchange in a real or reasonable time, classical analytical results,
which are computationally super-fast, can be directly used with a
sufficient accuracy as a part of such large codes.
Charge exchange and crossings of corresponding
energy levels that enhance charge exchange are of a great physical interest from
both fundamental and practical viewpoints. For example, charge exchange in high
temperature plasmas is strongly connected with problems of energy losses and of
plasma diagnostics. Specifically, charge exchange between multi-charged impurity
ions and hydrogen (or deuterium, or tritium) atoms in tokamaks provides a
nonlinear coupling of kinetics of impurities and neutrals, thus affecting the
feasibility of controlled fusion (since multi-charged ions produce considerably
more radiative losses per unit particle than singly charged ions of the nuclear
fuel components) - see, e.g., [1, 2] and references therein.
Charge exchange in tokamaks occurs at the presence
of relatively large electric fields. Indeed, at the electron density Ne
= 1015 cm-3, the most probable value of the ion
microfield is 6 – 8 kV/cm (depending on the effective charge Zeff).
More importantly: for example, 10 keV ions moving across a 10T magnetic
field experience larger electric fields: F=40 kV/cm for carbon ions,
F=35 kV/cm for oxygen ions.
The paradigm is that charge exchange is an
inherently quantal phenomenon [3]. Recently Prof. Eugene Oks from the Auburn
University (AL) disproved this paradigm [4, 5]. Based on first principles
without any model assumptions, he presented a purely CLASSICAL ANALYTICAL
description of anticrossings (avoided crossings) of energy terms (levels)
that lead to charge exchange [4, 5].
Fig. 1 (left). Classical energy terms of a
molecule, in which one electron is shared by two fully-stripped ions of charges
Z and Z': a typical dependence of the scaled (dimensionless) classical energy h
= (M/Z)2E on the scaled (dimensionless) internuclear distance r =
(Z/M2)R. Here M is the projection of the angular momentum on the
internuclear axis, E is the energy, R is the internuclear distance.
Fig. 2 (right). The trajectory of the bound
electron in the stable motion, corresponding to the lower and middle energy
terms in Fig. 1.
In [4, 5] he considered a ZeZ'-problem: one
electron shared by two fully-stripped ions of charges Z and Z'. His
analytical calculations of classical energy terms yielded astonishing
results:
1)
* there are several
(!) energy terms of the same symmetry - see Fig. 1 (the same symmetry means the
same projection M of the angular momentum on the internuclear axis);
2)
* two of these classical
energy terms undergo an anticrossing (represented by the V-shape crossing
in Fig. 1);
3)
* at large internuclear
distances, for one of the crossing terms the electron is centered at the
Z-ion, for the other crossing term – at the Z'-ion. Thus,
this situation classically depicts charge exchange.
For the stable motion, corresponding
to the lower and middle energy terms in Fig. 1, the trajectory of the bound
electron is a helix on the surface of a cone, with axis coincident with the
internuclear axis. In this helical state, the electron, while spiraling
on the surface of the cone, oscillates between two end-circles obtained via
cutting the cone by two parallel planes perpendicular to its axis (Fig. 2).
References:
[1] Rosmej, F.B., and Lisitsa, V.S.,
Phys. Lett. A 244, 401 (1998).
[2] Isler, R.C., and Olson, R.E., Phys. Rev.A 37,
3399 (1988).
[3] Hutchinson, I.H., Principles of Plasma
Diagnostics, Cambridge Univ. Press, Cambridge, 1987, p. 286.
[4] Oks, E., Phys. Rev. Letters 85,
2084 (2000).
[5] Oks, E., J. Phys. B 33, 3319
(2000).
Tokamak
(From Wikipedia, the free encyclopedia)
A tokamak is a
machine producing a
toroidal (doughnut-shaped)
magnetic field for
confining a
plasma. It is one of several types of
magnetic confinement devices and the leading candidate for producing
fusion energy. The term tokamak is a transliteration of the Russian
word Токамак which itself comes from the Russian words: "тороидальная
камера в магнитных катушках" (toroidal chamber
in magnetic coils, tocamac). It was invented in the 1950s by
Igor Yevgenyevich Tamm and
Andrei Sakharov.
The tokamak is characterized by azimuthal (rotational) symmetry and the use of
the plasma current to generate the helical component of the
magnetic field necessary for stable equilibrium. This can be contrasted to
another toroidal magnetic confinement device, the
stellarator, which has a discrete (e.g. five-fold) rotational symmetry and
in which all of the confining magnetic fields are produced by external coils
with a negligible current flowing through the plasma.
A split image of the
largest tokamak in the world, the
JET,
showing hot plasma in
the right image during a shot.
History
While research into
nuclear fusion was conducted after
World War II, it was done under
classified programs. It was not until after the 1955
United Nations
International Conference on the Peaceful Uses of Atomic Energy in Geneva
that programs were declassified and scientists from different countries allowed
to collaborate.
In 1968, at the third
IAEA International Conference on Plasma Physics and Controlled Nuclear
Fusion Research at
Novosibirsk, Russian scientists announced that they had achieved electron
temperatures of over 1 keV (1
electron volt is equal to 11605
Kelvin) in a tokamak device. This stunned British and American scientists,
who were far away from reaching that benchmark. They remained suspicious until
tests were done with laser scattering a few years later, confirming the original
temperature measurements.
Since this performance
was far superior to any of their previous devices, most fusion research programs
quickly switched to using tokamaks. The tokamak continues to be the most
promising device for generating net power from nuclear fusion, reflected in the
design of the next generation
ITER device.
Why doughnut shaped?
The distinctive shape of
the fusion reactor is necessary in order to produce a magnetic field with as few
irregularities as possible. The
doughnut has a particular topological property that a
sphere (for example) does not have. The problem is referred to as the
hairy ball theorem. Imagine a sphere with hair growing out of it. The hair
is analogous to the magnetic field lines needed in a fusion reactor. It turns
out that it is impossible to comb hair on a sphere so that no hair sticks up. A
strand of hair that is standing on end would be equivalent to an instability in
the reactor. However, a hairy doughnut can be so combed, and thus adjustments to
the magnetic field can be made to correct the irregularities. This allows the
magnetic field to better confine the plasma.
<-- Tokamak magnet field
and current
Experimental tokamaks -- In
operation:
*
TFTR,
Princeton University,
USA; in operation from 1982 until 1997
*
Joint European Torus, in
Culham,
United Kingdom; 16 MW; in operation since 1983
*
JT-60, in
Naka,
Ibaraki Prefecture,
Japan; in operation since 1985
*
T-15, in
Russia; 10 MW; in operation from 1988 until 2005
*
Tore Supra
[1], at the
CEA,
Cadarache,
France; in operation since 1988
*
D3D, in
San Diego, USA; operated by
General Atomics since the late 1980s
*
START and
MAST in Culham, United Kingdom; START in operation from 1991 until 1998,
MAST in operation since 1999
*
Alcator C-Mod,
MIT; USA
[2]; in operation since 1992
*
HT-7 in
Hefei,
China; in operation since 1995; and HT-7U (EAST)
since 2006
*
FTU in
Frascati,
Italy; in operation since 1990
*
TCV,
EPFL,
Switzerland
Experimental tokamaks --
Planned:
* ITER, in
Cadarache,
France; 500 MW; start of operation expected in 2016
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