By R. Miller
An severe charged particle beam might be characterised as an equipped charged particle stream for which the results of beam self-fields are of significant value in describing the evolution of the move. study using such beams is now a swiftly transforming into box with vital purposes starting from the advance of excessive energy assets of coherent radiation to inertial confinement fusion. significant courses have now been validated at numerous laboratories within the usa and nice Britain, in addition to within the USSR, Japan, and several other japanese and Western eu countries. additionally, comparable study actions are being pursued on the graduate point at a number of universities within the US and out of the country. whilst the writer first entered this box in 1973 there has been no unmarried reference textual content that supplied a wide survey of the real issues, but contained adequate aspect to be of curiosity to the energetic researcher. That state of affairs has continued, and this e-book is an try to fill the void. As such, the textual content is aimed toward the graduate pupil, or starting researcher; notwithstanding, it comprises abundant details to be a handy reference resource for the complicated worker.
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Extra info for An Introduction to the Physics of Intense Charged Particle Beams
3) where e is the electron energy, EF is the energy of the Fermi level, k is the Boltzmann constant, Ii = h j2'fT where h is Planck's constant, and T is the absolute temperature. 4) An approximate form for the effective one-dimensional potential is (see Fig. 5) 36 Chap. 85XlO- 12 flm is the permittivity of free space (MKS units). The three contributions to the effective potential are (i) some constant value (- Wo) within the metal which is lower than the Fermi level, (ii) a contribution (- eEz) arising from an applied electric field, and (iii) a contribution - e 2/4u p 7T due to the image charge induced on the surface of the metal by an electron outside the metal.
48) In the parapotential model, the current flowing in the diode is calculated using Eq. 49) where S is a surface of constant r, and r is the curve of constant rand 0 bounding this surface. J( 0) is, therefore, the total current flowing within the Sec. 3 • Eledron Flow in High-Power Diodes 49 angle O. Thus lr B . ,. and E(J from Eqs. 38) and making the transformation from cp to y [Eq. 51 ) Performing the indicated differentiation of y with respect to 0 [Eq. 52) For large diodes an excellent approximation to the geometrical factor may be derived by noting that tanOm/2=(l-cosOm)jsinOmR:ll-cotOm=ld Ire' Expanding the logarithm gives [-In(tanOmI2)]-1 R:lrcld.
38) into Eq. 43) 48 Chap. 44) may be solved by elementary differential equation methods. 45) while the integration of Eq. 46) In the parapotential model, it is not necessary that the electron flow patterns extend to the anode; however, since it may be shown that the beam current is maximized in this instance it will be assumed that the flow patterns do extend completely to the anode. 47) where Om denotes the angle of the (conical) cathode surface. Substituting these boundary conditions into Eq.