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I. D. Kaganovich, |
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Plasma Physics Laboratory Princeton University |
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Study propagation of a high-current
finite-length ion beam in a plasma |
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Prediction of |
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Degree of charge neutralization |
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Degree of current neutralization |
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Self electric and magnetic fields |
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Heavy ion fusion |
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Plasma lenses |
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Cosmic rays |
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Inertial fusion is based on h-bomb design |
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Who built the h-bomb? Debate revives |
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By WILLIAM J. BROAD, April 24, 2001 |
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Total beam energy--5 MJ. |
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(~10 kg heated on 100C, 1kg trinitrotoluene
TNT). |
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Focal spot radius--3 mm. |
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Ion range--.1 g/cm^2 (1 mm in typical
materials). |
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Pulse duration--10 ns. |
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Peak power--400 TW. |
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Forty times the average world-wide electric
power consumption. |
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Ion energy--10 GeV. |
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Current on target--40 ka (total). |
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Ion mass--200 amu. |
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From ~3cm at chamber entry to 1-2 mm at target |
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Ion beam density varies 1011cm-3 to 1013cm-3 |
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Flibe density 1013cm-3 |
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Plasma produced by beam or photo ionization or
external source |
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Beam
Radius at the target as function of degree of neutralization |
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Different from well-studied electron beams in a
background plasma |
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Clearer physical picture is required for degree
of charge and current neutralization for ion beams of finite length in a
background plasma |
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Nonlinear theory |
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Numerical simulation: |
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Particle in cell |
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Fluid |
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Neutralization experiment (VNL) |
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Fully electro-magnetic relativistic
particle-in-cell (PIC) code. |
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Non-relativistic Darwin model for long beams. |
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The other code uses approximation of long beams:
beam length is much longer than beam radius; Therefore beam can be
described by a number of weakly interacting slices. |
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A 2D electromagnetic PIC code uses a leap-frog,
finite-difference scheme to solve Maxwell's equations on a 2D rectangular
grid in the frame moving with the beam. The current deposition scheme is
designed to conserve charge exactly, so there is no need to solve Poisson's
equation. |
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Approximation of long beams: |
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Beam
length is much longer than beam radius; |
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Therefore, beam can be described by a number of
weakly interacting slices. |
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The electric field is found from radial
Poisson’s equation. |
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As a result of the simplification the second
code is hundreds times faster than the first one and can be used for most
cases, while the first code provides benchmarking for the second. |
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If you would like to eat something delicious,
bite in small pieces |
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Steady-state ion beam propagation in a
pre-formed cold stationary uniform infinite plasma |
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Important issues |
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Finite length of the beam pulse |
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Arbitrary value of nb / np (nb>>np) |
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2d |
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Approximations |
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Fluid approach, |
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Conservation of generalized vorticity |
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Long dense beams lb >> rb
, Vb/wp |
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Exact analytical solution |
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Electron density |
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Left – PIC, |
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Right -
fluid |
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Brown lines: electron trajectory in the beam
frame |
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Red line: ion beam size |
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Normalized magnetic field |
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The analytical solutions for the electric and
magnetic fields generated by an ion beam pulse have been determined in the
nonlinear case for arbitrary values of np/nb under
the assumption of a long beams lb>>rb |
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Under these conditions a problem is essentially
1D ODE for each beam slice , takes few minutes to obtain numerical solution |
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The study of entry and exit of ion beam from the
plasma is now being done |
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