John Barnard Steven Lund USPAS June 13-24, 2011 Melville, NY Current limits A. Axisymmetric 1. Solenoids 3. Einzel lens B. Quadrupolar 1. Derivation of envelope equations with elliptic symmetry 2. Current limit using fourier transform method 3. Alternative methods
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John Barnard!
Steven Lund!
USPAS!June 13-24, 2011!
Melville, NY!
Current limits!
A." Axisymmetric!1." Solenoids!
3." Einzel lens!
B." Quadrupolar!
1." Derivation of envelope equations with ! elliptic symmetry!
2. Current limit using fourier transform!
method!
3. Alternative methods!
r
The Heavy Ion Fusion Virtual National Laboratory!
Schematic of Einzel lens
!= -V +V -V +V -V +V -V +V -V!2L!
Insulators!
Electrodes!
Beam!
Beam envelope
2 4 6 8
!1.0
!0.5
0.5
1.0Potential lines
2 4 6 8
!1.0
!0.5
0.5
1.0
2 4 6 8
!1.0
!0.5
0.5
1.0
2 4 6 8
!1.0
!0.5
0.5
1.0
φ and Δrb and Δv''z
Er and φ'' and Δvz
Δv'z and Ez and Δrb'
-
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