PHYSICAL REVIEW E VOLUME 53, NUMBER 3 MARCH 1996 Measurement of the Coulomb energy loss by fast protons in a plasma target G. Belyaev, M. Basko, A. Cherkasov, A. Golubev, A. Fertman, I. Roudskoy, S. Savin, B. Sharkov, and V. Turtikov Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya 25, 117259Moscow, Russia A. Arzumanov, A. Borisenko, I. Gorlachev, and S. Lysukhin Institute for Itluclear Physics, National nuclear Center of Kazakhstan, 480082 Alma Ata-, Kazakhstan D. H. H. Hoffmann and A. Tauschwitz Gesellschaft fur Schwerionenforschung (GSI), Postfach 110552, D 64220 D-armstadt, Germany (Received 6 October 1995) We report measurements of the energy loss by 1-MeV protons in a plasma target created by electric discharge in the hydrogen gas. Combined with independent measurements of the mean ionization de- gree and the electron areal density of the plasma column, based on two-wavelength laser interferometry, the energy-loss data let us infer the value of the Coulomb logarithm: Lf, =14. 9+2. 8 for the stopping power of the free plasma electrons. This value is 3. 1+0.6 times higher than that given by the Bethe for- mula for the neutral hydrogen and, within the experimental errors, agrees with the theoretical predic- tions. PACS number(s): 52.40. Mj, 34.50. Bw I. INTRODUCTION dE dE dE dX dX b dX dE dx In the nonrelativistic limit, ignoring the usually small contribution due to the plasma ions, the stopping power for our purposes can be written as The investigation of the interaction of ionizing radia- tion with matter has always been a classical topic of atomic and nuclear physics. Due to a wide range of ap- plications, there still is a growing need for a deeper un- derstanding of physical processes that determine the stopping of fast ions in matter. A large amount of experimental data have been accu- mulated concerning the stopping of fast ions in cold matter under normal conditions, when the energy loss is dominated by inelastic collisions with bound electrons [1]. At the same time, very few data have been obtained on stopping of ions in plasmas, where the theory predicts a considerable enhancement of the Coulomb energy losses in collisions with free plasma electrons. This pro- vides the principal motivation for the present work. Assuming that the beam of fast ions is sufficiently di- lute and no collective processes such as the beam-plasma instability contribute to the stopping, the beam energy losses can be evaluated in the single-particle approxima- tion. In general, the Coulomb stopping power of partially ionized rnatter for a pointlike ion can be represented as the sum of contributions due to bound electrons (be), free plasma electrons (fe), and free plasma ions (fi): 4me pro Zdt (Z, — z')Lb, +z*o Lt, I, U 3, Ue where Xo is the Avogadro number, Z, and A, are, re- spectively, the atomic number and mass of target atoms, p is the target density, z* is the mean ionization degree of the target material, U, is the thermal velocity of free tar- get electrons, U and Z, z are, respectively, the velocity and the eff'ective charge of the fast ion. The Chandrasekhar function 6 (U/U, ) originates from averaging the relative velocity of the fast ion with respect to the target electrons over the Maxwellian distribution. The value of G approaches unity for U ))U, — which is al- ways the case for situations considered below — and goes to zero as (U/U, )' at v « U, . The Coulomb logarithms L, b, and L, f, for the bound and free electrons, respectively, appear as a result of in- tegration of the Rutherford cross section over the relevant range of impact parameters or, equivalently, over the relevant range of transferred momenta. In gen- eral, when L ))1, the Coulomb logarithm can be ex- pressed as L =ln(p, „/p;„), where p, „=2m, u is the maximum transferred momentum, and p;„ is the minimum transferred momentum below which the Ruth- erford formula becomes inapplicable due to either atomic binding or plasma screening. In contrast to p „, calculation of p;„ is not trivial, and the answer depends on whether the classical or quan- tum limit applies to the Coulomb scattering of target electrons by the fast ion. The division line between the 1063-651X/96/53(3)/2701(7)/$10. 00 53 2701 1996 The American Physical Society