High Energy Ion Energy Depletion Model in HYDRA Page: 4 of 4
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2
where Zbo is the energetic ion atomic number,
Betz = CBetz b e
and
CBetz 1/aZ609
and ca is the fine structure constant.
(b and /3e are the light speed normed velocities of the energetic ion and
thermal electrons given by b = 1 - 1/i[ and /3 = 1 - 1/ye with Yb =
1 + E6/Mp and Ye = 1 + Te/Me.
The quantity RBF, the ratio of bound to free electrons is
RBF = /Z*- 1
where Z and Z* are the background (target) effective and average charge
state averaged over the mass fractions of the ionic (target) mix. Note that
at full ionization Z* -- Z so RBF -+ 0 and the bound electron contribution
vanishes, while for vanishing ionization, since ne ~ Z* the bound electron
contribution varies as neRBF ~ Z - Z*.
Defining the (small) ratio R3 = 1e/,b we write the coefficient of the ion
energy loss due to free electrons CG as
Cr = 1/(1 - R8(.1263R6(.1195 - 1.5075R1))).
This derives from an expansion of G(x) = erf(x) - x erf'() for r 1. The
remaining terms AB and AF, the Coulomb logarithms for bound and free
collisions, are given as
AB = ln(1 + 2Mec2 3b/I) + ln'yb - = ln(1 + 102200 3/Z) + nyb - b
and
21.376X1016 .
AF = ln(1 f 6 ) + .5(ln -yb - # ).
where I = Z/102200 is the average ionization potential for bound electrons
and in 'Yr - ,i is a relativistic correction factor in both Coulomb logarithms.
The depletion equation is initialized at Eb = Eo for each energetic ion
beamlet and tracked until Eb < Ebfloor, at which point all the remaining
energy is deposited (ie. in the Cell where this condition first occurs).
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Kerbel, G & Prasad, M. High Energy Ion Energy Depletion Model in HYDRA, report, June 29, 2007; Livermore, California. (https://digital.library.unt.edu/ark:/67531/metadc870571/m1/4/: accessed April 23, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.