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'

-