From: Alberto Fasso' (fasso@SLAC.Stanford.EDU)
Date: Wed Apr 18 2007 - 02:49:08 CEST
You say "no electromagnetic shower should develop", and I guess that you
you have "derived the dE/dx from FLUKA", based on the energy deposited in
the target, which is 2.7 MeV (indeed 2.7/(8.96 * 0.2) = 1.5, as you report).
But try to score what escapes from the target (in addition to the primary
electrons, of course), and you will find, per each incident 1.5 TeV electron:
0.687 electrons with a total energy of 669 GeV
0.044 positrons with a total energy of 4.7 GeV
0.891 photons with a total energy of 179 GeV
(compare these large escaping energies with only 2.7 MeV deposited in the
All that energy is LOST by the primary electron but not DEPOSITED inside
the target. Maybe that is not a fully developed shower, but there is a lot
of multiplication. The target must be much much thinner if you want to
calculate a simple dE/dx.
But even with a very thin target, keep in mind that Bethe's theory gives you
the energy lost, but not the energy deposited. Energetic delta rays will escape
from the target, so the energy deposited will always be less than the energy
lost. You should not compare with Bethes dE/dx, but with Bethe's RESTRICTED
dE/dx, which however I don't think has been tabulated by Seltzer and Berger.
On Mon, 16 Apr 2007, Arnaud Ferrari wrote:
> I have just started using FLUKA in order to calculate energy deposition in
> a dump window at CLIC. I have simulated a simple problem: a 1.5 TeV electron
> beam passing through a 2 mm thick copper layer. Since the radiation length of
> copper is 1.4 cm, no electromagnetic shower should develop. From FLUKA I have
> derived that 1/rho.(dE/dx) = 1.5 MeV/g.cm-2. This roughly corresponds to the
> energy loss of a minimum ionizing particle in copper. Note that I use default
> values for all cards in that case...
> When using the analytical formulas of Seltzer and Berger, Int. J. Appl.
> Radiat. Isot. Vol. 35, No. 7 (1984), based on Bethe's stopping power and
> Sternheimer's theory of the density effect, 1/rho.(dE/dx) = 2.3 MeV/g.cm-2
> in copper instead, i.e. about 50% more losses than for a minimum ionizing
> I therefore wonder about the discrepancy between FLUKA and the paper. Is it
> possible that not all interactions/effects are included in FLUKA? Or is that
> paper not relevant for such high-energy electrons?
> I hope that some experts could discuss this issue with me.
> Thanks and best greetings,
> Dr. Arnaud Ferrari
> IKP, box 535, 75121 Uppsala, Sweden
-- Alberto Fasso` SLAC-RP, MS 48, 2575 Sand Hill Road, Menlo Park CA 94025 Phone: (1 650) 926 4762 Fax: (1 650) 926 3569 email@example.com
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