By R. Miller

An extreme charged particle beam might be characterised as an prepared charged particle stream for which the consequences of beam self-fields are of significant significance in describing the evolution of the stream. examine using such beams is now a speedily turning out to be box with very important functions starting from the improvement of excessive strength resources of coherent radiation to inertial confinement fusion. significant courses have now been validated at a number of laboratories within the usa and nice Britain, in addition to within the USSR, Japan, and a number of other jap and Western eu countries. furthermore, similar study actions are being pursued on the graduate point at numerous universities within the US and overseas. while the writer first entered this box in 1973 there has been no unmarried reference textual content that supplied a large survey of the real themes, but contained adequate element to be of curiosity to the lively researcher. That scenario has endured, and this ebook is an try to fill the void. As such, the textual content is aimed toward the graduate scholar, or starting researcher; besides the fact that, it comprises plentiful details to be a handy reference resource for the complex worker.

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**Example text**

5 can be observed when an electron beam is injected into a neutral gas at various background pressures (Fig. 16, 17 At very low pressures the beam-generated ionization is small (fe = 1m = 0), and the beam expands radially. At somewhat higher pressures, Ie > '1- 2 , but the conductivity remains too low to provide significant current neutralization (1m = 0), and pinched beam propagation is observed. 5. Beam Behavior for Various Values of the Charge and Current Neutralization Fractions 1m/Ie o o Expands Equilibrium Contracts Equilibrium Sec.

A IE L 0,---------------::11 z w ..... ~ -¢Jo ,,_~..... 42

22) Combining Eqs. 24) Eq. 25) Sec. 26) Integration of Eq. 27) The constant of integration C 1 is zero becausey = dy/dz = df/>/dz =0 at the cathode. Taking the square root and integrating, Eq. 29) where 8=cos - 1[1_(y2_ 1)1/2] 1+( y2 + 1)1/2 F( 8, Ii /2) and E( 8, Ii /2) are elliptic integrals of the first and second kind, defined by Substituting for K and solving Eq. 28) for J yields the relationship between current density and the applied voltage for the relativistic planar Chap. 32) where d is the electrode spacing and Yo corresponds to the applied potential Icf>ol.