


I. D. Kaganovich, 

Plasma Physics Laboratory Princeton University 





Study propagation of a highcurrent
finitelength ion beam in a plasma 

Prediction of 

Degree of charge neutralization 

Degree of current neutralization 

Self electric and magnetic fields 




Heavy ion fusion 

Plasma lenses 

Cosmic rays 






Inertial fusion is based on hbomb design 



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By WILLIAM J. BROAD, April 24, 2001 









Total beam energy5 MJ. 

(~10 kg heated on 100C, 1kg trinitrotoluene
TNT). 

Focal spot radius3 mm. 

Ion range.1 g/cm^2 (1 mm in typical
materials). 

Pulse duration10 ns. 

Peak power400 TW. 

Forty times the average worldwide electric
power consumption. 

Ion energy10 GeV. 

Current on target40 ka (total). 

Ion mass200 amu. 








From ~3cm at chamber entry to 12 mm at target 

Ion beam density varies 10^{11}cm^{3} to 10^{13}cm^{3} 

Flibe density 10^{13}cm^{3} 

Plasma produced by beam or photo ionization or
external source 




Beam
Radius at the target as function of degree of neutralization 




Different from wellstudied electron beams in a
background plasma 

Clearer physical picture is required for degree
of charge and current neutralization for ion beams of finite length in a
background plasma 





Nonlinear theory 

Numerical simulation: 

Particle in cell 

Fluid 

Neutralization experiment (VNL) 





Fully electromagnetic relativistic
particleincell (PIC) code. 

Nonrelativistic Darwin model for long beams. 

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. 




A 2D electromagnetic PIC code uses a leapfrog,
finitedifference 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. 





Approximation of long beams: 

Beam
length is much longer than beam radius; 

Therefore, beam can be described by a number of
weakly interacting slices. 

The electric field is found from radial
Poisson’s equation. 

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. 




If you would like to eat something delicious,
bite in small pieces 



Steadystate ion beam propagation in a
preformed cold stationary uniform infinite plasma 







Important issues 

Finite length of the beam pulse 

Arbitrary value of n_{b} / n_{p }(n_{b}>>n_{p}) 

2d 

Approximations 

Fluid approach, 

Conservation of generalized vorticity 

Long dense beams l_{b} >> r_{b}
, V_{b}/w_{p} 

Exact analytical solution 






Electron density 

Left – PIC, 

Right 
fluid 

Brown lines: electron trajectory in the beam
frame 

Red line: ion beam size 





Normalized magnetic field 








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 n_{p}/n_{b }under
the assumption of a long beams l_{b}>>r_{b} 

Under these conditions a problem is essentially
1D ODE for each beam slice , takes few minutes to obtain numerical solution 

The study of entry and exit of ion beam from the
plasma is now being done 
