To advance
understanding of complex processes of plasma and particle beams
self-organization, theoretical (analytical) study should be combined with
the development of efficient and rigorous
computational tools to test new models and theories. One
of the examples of the optimal synthesis of main methods of physical
investigation theory and numerical simulations is development of fast
simulation techniques, which are based on analytical methods applied to
physical system to eliminate small temporal or spatial scales. The
accelerator and plasma physics are typically characterized by wide disparity
of temporal or spatial scales with many orders of magnitude difference
between smallest and largest scales. The disproportion in scales presents
great challenge for direct numerical simulation, when the smallest scales
have to be resolved. Analytical methods permit eliminating smallest temporal
or spatial scales by averaging over fastest time scales and allowing
discontinuities of plasma profile, which male it possible to neglect small
spatial scales. Let me give few examples of how these ideas were
applied to various accelerator and plasma physics problems.
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High-energy density
plasma physics
Ion beam-plasma
interaction
The charge and
current neutralization of an ion beam propagating in a preformed plasma
have been studied. Application of the conservation law of generalized
vorticity and making use of a small parameter - ratio of the beam radius to
the beam length allowed reducing system of equations and developing robust
computational tool for simulation of beam plasma interaction. To check the
theoretical predictions and benchmark particle-in-cell code, a
two-dimensional electromagnetic fluid code was developed, which can predicts
in few minutes, whereas full scale particle-in-cell code requires much
longer computational times and resources. Movies generated from the code
results show complex phenomena occurring during beam entry into plasma and
exit from plasma.
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Atomic physics for
HEDP applications
The second example pertains to study of multiple electron
stripping of heavy ion beams. Heavy ion beams lose electrons while
passing through background gas in the target chamber, and therefore it is
necessary to assess the rate at which the charge state of the incident beam
evolves on the way to the target. Accelerators designed primarily for
nuclear physics or high-energy physics experiments utilize ion sources that
generate highly stripped ions in order to achieve high energies
economically. As a result, accelerators capable of producing heavy ion beams
of 10 to 40 Mev/amu with charge state 1 currently do not exist.
Hence, the stripping cross-sections used to model the performance of
heavy ion fusion driver beams have, up to now, been based upon theoretical
calculations. The cross sections are calculated using different techniques.
The Born approximation, which results in overestimate
of the cross sections, should be valid for Ze2<<hV,
where Z is the target atomic number and V
is the velocity of the beam ion relative to the target atom.
The classical trajectory calculations
do not account for tunneling transitions allowed by quantum mechanics.
Neither approach is expected to perform well across a wide spectrum of beams
and targets. Aspects of one approach must be combined with parts of the
other approach in order to address shortcomings in the underlying
assumptions. This was accomplished by using matching of different techniques
in their range of validity. The resulting theoretical values for cross
sections agree well with experimental data.
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Collective
effects and turbulence
The plasma is subject of numerous instabilities. For many
applications it is important to access rate of instabilities and nonlinear
stage of saturation and corresponding anomalous transport.
For low-pressure discharges most instabilities are
associated with particle production, mostly due to nonlinear dependence of
ionization frequency on electric field. The instability lead to
complicated two-three dimensional structure of discharges. Few examples for
dc and rf discharges have been studied.
For HEDP applications instability mainly occurs due to
motion of particle beams relative to background plasma. Intense beam propagating in plasma drive various plasma
instabilities: two-stream, Weibel's, Buneman's, etc.. The nonlinear stage of instabilities, saturation and
corresponding wave-turbulence is important and part of studies of HEDP
plasmas.
Low-temperature
plasmas and and gas-discharge physics
Kinetic effects and studies of non-Maxwellian electron
energy distribution functions
The modern trend in plasma technology aims at decreasing gas pressures down to mTorr
range. At these low pressures, it is easier to maintain uniform plasmas with
well-controlled parameters. In low-pressure plasmas the electron mean free
path can be larger or comparable to the plasma characteristic inhomogeneity
scale. Therefore, the electron
transport is collisionless and nonlocal, since an electron can traverse a
significant distance between collisions and sample different values of
electric field along its way. As
a result, the electron current is determined not by the local electric
field, but by the entire profile of the electric field.
Also for inhomogeneous electric fields another mechanism of heating
or power dissipation is possible, which is strikingly different from
collisional one; namely collisionless heating is determined by the
wave-particle resonances and independent of
the collision frequency. Moreover, the electrons are frequently not
in equilibrium with themselves, and as a result, the electron energy
distribution functions in such plasmas are typically non-Maxwellian. This
property makes plasmas a remarkable tool for plasma applications, including
plasma processing, lighting, plasma sources, thrusters, etc.
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Collisionless
heating and anomalous phenomena in plasmas
Due to the large value of mean free path, the
main mechanism of electron heating turns out to be a collisionless heating
rather than conventional Ohmic heating, which is dominant for higher
pressures. Therefore, a quantitative description has to be developed for collisionless
heating in nonuniform plasmas of low-pressure discharges. The role of collisions and non-linear effects was investigated; it was shown that collisions play an important
role even in collisionless heating as a decorrelation process. Under certain
conditions, collisionless heating is proportional to collision frequency due
to the influence of nonlinear effects. This is in contrast to the common
situation, where collisionless heating does not depend on collision
frequency, as in the classical theory of Landau damping and anomalous
skin effect.
Based on quasi-linear theory, a self-consistent treatment of
collisionless heating was performed for various types of low-pressure
discharges and thrusters. This system includes the kinetic
equation for the electron distribution function in self-consistent electric
field. Straightforward numerical modeling of such system is quite
complicated. An effective semi-analytical method of solving this system was
developed. The principles of fast modeling of low-pressure discharges are
based on averaging over fast electron and ion motions and eliminating a
small spatial scale, the Debye radius. As a result, the solution of a
self-consistent system of the electron kinetic equation, the Poisson
equation, and the ion continuity equation is approximately hundreds times
faster compared with straightforward numerical techniques.
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Transport in
multi-component plasmas
Transport in multi-component plasma is very different from a
transport of plasma comprising from only electrons and ions. In
particularly, the multi-component plasma tend to stratify into region of
different composition, completely opposite to the naive first assumption.
The negative ion fronts of sharp gradient of negative ion density was shown
to to form during all stages of plasma evolution: ignition,
steady-state and afterglow.
Transport in
magnetized plasmas
The ambipolarity condition for electron and ion transport in
magnetized plasma in two dimensions causes rather complicated flow patterns. Electrons
can flow fast along the magnetic field lines and simultaneously diffuse
radially far then come back along another
magnetic field lines. As a result, ions can flow freely to the radial position
where electrons are available due to such complex loop-like electron
trajectories. An example of such transport is plasma jet’s radial expansion in presence of strong axial magnetic
field. The "conventional wisdom" approach predicts a conical shape for
the plasma jet. This stems from the assumption that electrons and ions
diffuse together across the magnetic field lines with an effective ambipolar
diffusion coefficient taking from one-dimensional theory. However, such
"conventional wisdom" approach fails in two-dimensional geometry,
because electrons and ions trajectories are very different in 2D. The short-circuiting
electron flows result in a cylindrical shape of
the jet in contrast to conical.
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