Perveance

Introduction

Perveance is a notion used in the description of charged particle beams. The value of perveance indicates how significant is the space charge effect on the beam’s motion. The term is used primarily for low-energy electron beams, which motion is often dominated by the space charge.

Origin of the word

The word was probably created from Latin "pervenio" – to attain.

Definition

For an electron gun, the gun perveance $mathbf\{P\}$ is determined as a coefficient of proportionality between a space-charge limited current, $mathbf\{I\}$, and the gun anode voltage, $mathbf\{U\_a\}$, in three-half power in the Child- Langmuir law [1]

$\{I\}\; =\; \{P\}cdot\; \{U\_a\}^frac\{3\}\{2\}$

The same notion is used for non-relativistic beams propagating through a vacuum chamber. In this case, the beam is assumed to have been accelerated in a stationary electric field so that $mathbf\{U\_a\}$ is the potential difference between the emitter and the vacuum chamber, and the ratio of $frac\{mathbf\{I\{mathbf\{U\_a\}^frac\{3\}\{2$ is referred to as a beam perveance. In equations describing motion of relativistic beams, contribution of the space charge appears as a dimensionless parameter called the generalized perveance $mathbf\{K\}$ [2] defined as

$\{K\}\; =\; frac$II_0cdotfrac{f{2eta}^3{gamma}^3}cdot (1-gamma^2f_c),

where $\{I\_0\}=4pivarepsilon\_\{0\}cdotfrac\{m\; c^3\}\{e\}$ = 17 kA is Budker current; and $mathbf\{gamma\}$ are the relativistic factors, and $mathbf\{f\_c\}$ is the neutralization factor.

References

1. Handbook of Accelerator Physics and Engineering, edited by A.W. Chao and M. Tigner, World Scientific, 1999, p.100
2. M. Reiser, Theory and Design of charge particle beams, John Wiley & Sons, Inc., 1994 categorized=Accelerator neutrino experiments