Velocity of the plasma surface also named the hb

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: al., 1992; Robinson, Gibbon, Zepf et al., 2009; 16 The electromagnetic theory of radiation pressure is due to James Clerk Maxwell (1873). It is, however, interesting that the Italian physicist Adolfo Bartoli (1884) also independently obtained Maxwell’s result in 1875 from thermodynamic considerations. Andrea Macchi, Marco Borghesi, and Matteo Passoni: Ion acceleration by superintense laser-plasma . . . 774 Schlegel et al., 2009). In the instantaneous frame where the surface is at rest we observe incoming ions with density ni HB and velocity ÀvHB bouncing back at the surface. The EM momentum flow, i.e., the radiation pressure, must then balance a momentum flow difference equal to ni HB ð2mi HB vHB ÞvHB with HB ¼ ð1 À v2 =c2 ÞÀ1=2 . In this reference frame, the HB radiation pressure is Prad ¼ ð2I=cÞð1 À vHB =cÞ=ð1 þ vHB =cÞ as demonstrated by a Lorentz transformation.17 The global momentum balance thus gives18 2I 1 À vHB =c ¼ ni HB ð2mi HB vHB ÞvHB : c 1 þ vHB =c (28) Solving for vHB yields vHB Å1=2 ¼ ; c 1 þ Å1=2 ż I Z nc me 2 ¼ a: mi ni c3 A ne mp 0 (29) The fastest ions are those bouncing back from the surface in the moving frame, resulting in a maximum energy per nucleon in the laboratory frame Å : (30) 1 þ 2Å1=2 In the nonrelativistic regime where Å ( 1 and vHB ( c, we obtain vHB =c ’ Å1=2 and E max ’ 2mp c2 Å. Essentially the same results are obtained with a dynamical model of ion acceleration in the charge separation region at the surface (Macchi et al., 2005). Such model and related PIC simulations show that the ions pile up at the end of the skin layer producing a sharp density spike and causing hydrodynamical breaking and collapse of the electron equilibrium. This process leads to the production of a narrow bunch of fast ions at the velocity 2vHB which penetrates into the plasma bulk. Eventually the quasiequilibrium condition is established again and the process repeats itself as long as the laser pulse is on. HB acceleration is thus of pulsed nature, although on the average it may be described by a steady model (Schlegel et al., 2009).19 Equation (30) indicates that with present-day intensities high energies may be obtained via HB acceleration if the density can be reduced to be slightly above nc , which is possible if a gas jet target and a long wavelength laser, i.e., CO2 , is used. This scheme would be interesting for E max ¼ 2mp c2 17 Note that the relativistic correction is equivalent to account for the energy depletion of the incident radiation in the adiabatic approximation. This can easily be shown by the heuristic model of radiation pressure as resulting from the reflection of a number N ^ (per unit surface) of photons with energy momentum ðℏ!; xℏ!=cÞ contained in a short bunch of duration , corresponding to an intensity I ¼ N ℏ!=. If the surface is moving at velocity V ¼ c, the frequency of the reflected photons is !r ¼ !ð1 À Þ=ð1 þ Þ and the reflection time is r ¼...
View Full Document

This document was uploaded on 09/28/2013.

Ask a homework question - tutors are online