Abstract
This letter presents a two-dimensional (2D) model of space-charge-limited current in a planar crossed-field gap with a magnetic strength of
B
∕
B
H
=
0
-
3
, where
B
H
is the Hull cutoff mag
netic field. The electrons are emitted from an infinite length strip of finite width
W
com
parable to the gap spacing
D
. It is found that the 2D enhancement of the crossed-field limiting current is
1
+
F
×
4
D
∕
(
π
W
)
, where
F
(
=
0.05
-
0.5
)
is a normalized mean-position factor, and it is a function of
B
∕
B
H
. Good agreement has been obtained in comparisons with particle-in-cell simulation.