User:Perveance

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[edit] Introduction

Perveance is a notion used in a description of charge 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 space charge.


[edit] Origin of the word

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


[edit] 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]

\mathbf{I} = \mathbf{P}\cdot \mathbf{U_a}^\frac{3}{2}

The same notion is used for a non-relativistic beam propagating through a vacuum chamber. Assuming that the beam was accelerated in stationary field, Ua in this case 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 generalized perveance \mathbf{K} [2] defined as

\mathbf{K} = \frac{\mathbf{I}}{\mathbf{I_0}}\cdot frac{\mathbf{2}}{\mathbf{I_0}}\cdot \mathbf{U_a}^\frac{3}{2} K = I/I0 * 2/(beta^3*gamma^3) * (1-gamma^2*fc),

where I0 = 4*pi*eps0*m*c^3/e = 17 kA is Budker current; Beta and Gamma are the relativistic factors, and fc is the neutralization factor.


[edit] 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