SUPERTHERMAL ELECTRON DISTRIBUTION Page: 4 of 9
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the electron flux with the radiated energy per electron, the x-ray fluence,
F(hv) is given by
F(hv) = ATN dE n(E) fy d y(E ,h(v) ,
Wvhv dl(Ej ) E
where A is the area of the electron flux and T is the characteristic plasma
time. The expression is, in general, not integrable, but if suitable ap-
proximations are made for o(E', hv) and x (E') analytic results can be ob-
The bremsstrahlung cross-section is given in the Bethe-Heitler approxi-
BH(Eb)[ = hh (1 + (1 hv1/2 2
o = - = 7.90 x 10 cm2 - eV.
By comparison the classical expression for bremsstrahlung is4
class (Eh E) (5)
The ratio of the Bethe-Heitler cross-section to the classical expression is
oBH(EJ- ) E-- 1 + - E /2
nClass(E 1 (1h- E
and the ratio of the total energy radiated is
BH(E, hv) ' hv d(hj)
JOClass(E, hv) - hu d(hv)
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Kauffman, R. SUPERTHERMAL ELECTRON DISTRIBUTION, report, December 20, 2007; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc899020/m1/4/: accessed February 17, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.