Ion Acceleration by Collisionless Shocks in High-Intensity- Laser–Underdense-Plasma Interaction M. S. Wei, 1 S. P. D. Mangles, 1 Z. Najmudin, 1 B. Walton, 1 A. Gopal, 1 M. Tatarakis, 1, * A. E. Dangor, 1 E. L. Clark, 1,2 R. G. Evans, 1,2 S. Fritzler, 3 R. J. Clarke, 4 C. Hernandez-Gomez, 4 D. Neely, 4 W. Mori, 5 M. Tzoufras, 5 and K. Krushelnick 1 1 Blackett Laboratory, Imperial College, London, SW7 2BZ, United Kingdom 2 Plasma Physics Department, Atomic Weapons Establishment plc, Aldermaston, Reading RG7 4PR, United Kingdom 3 Laboratoire d’Optique Applique ´e, E ´ cole Polytechnique, ENSTA, Palaiseau, France 4 Central Laser Facility, Rutherford Appleton Laboratory, Chilton, Oxon, OX11 0QX, United Kingdom 5 Department of Physics and Astronomy and of Electrical Engineering, UCLA, Los Angeles, California 90095, USA (Received 24 February 2004; published 7 October 2004) Ion acceleration by the interaction of an ultraintense short-pulse laser with an underdense-plasma has been studied at intensities up to 3  10 20 W=cm 2 . Helium ions having a maximum energy of 13:2  1:0 MeV were measured at an angle of 100  from the laser propagation direction. The maximum ion energy scaled with plasma density as n 0:700:05 e . Two-dimensional particle-in-cell simulations suggest that multiple collisionless shocks are formed at high density. The interaction of shocks is responsible for the observed plateau structure in the ion spectrum and leads to an enhanced ion acceleration beyond that possible by the ponderomotive potential of the laser alone. DOI: 10.1103/PhysRevLett.93.155003 PACS numbers: 52.38.Kd, 52.38.Hb, 52.65.Rr Throughout the past decade, continuing developments in high-intensity, short-pulse laser technology have stimulated significant interest in electron acceleration using laser-produced plasmas. This is important for ap- plications such as compact particle accelerators [1,2] and fast ignition for inertial confinement fusion [3]. In addi- tion, ions can be accelerated by the strong space charge field generated by the transverse ponderomotive force of the laser which expels electrons from the region where the laser beam is intense [4,5]. Study of the ion dynamics is important as it can supply valuable information of the fundamental physics of the interaction of a high-intensity laser with underdense plasma, such as self-focusing and channelling due to relativistic and charge displacement effects [6–9]. It is also directly related to the observations of anomalously high yields of neutrons resulting from hot channel formation [10,11]. The maximum ion energy that can be produced by this process is roughly equal to the ponderomotive energy. Krushelnick et al. [4] have ob- served helium ions with peak energies of 3.6 MeV , deu- terons up to 1 MeVand neon ions with energy greater than 6 MeV. From the maximum ion energy measurements, it was inferred that the peak laser intensity in the experi- ments was a few times the focused intensity in vacuum due to self-focusing of the high-intensity laser in plasma. This Letter presents measurements of energetic ions accelerated during the interaction of a 0.25 PW laser with a gas-jet plasma at electron densities up to 1:4  10 20 cm 3 . Thus P L =P c is greater than 2000, where P L is the laser power and P c is the critical power required for relativistic self-focusing to dominate diffraction, which is given by P c  17:4n c =n e  GW, where n e is the plasma density and n c is the critical density. The vacuum inten- sity of the laser was up to 3  10 20 W=cm 2 , which corre- sponds to a normalized vector potential a 0  eE= mc! 0  15. Helium ions with energy up to 13:2  1:0 MeV are measured in a direction of 100  from the laser axis. A strong correlation is observed between the maximum ion energy and the initial plasma density. The ion energy spectrum at high density shows a well defined plateau structure. Particle-in-cell (PIC) simulations indi- cate that the plateau is produced by the interaction of multiple radial electrostatic shocks produced by the trans- verse ponderomotive force, which act as an additional acceleration mechanism. The experiments were performed using the VULCAN Petawatt laser beam line at the Rutherford Appleton Laboratory. For these investigations, the laser produced pulses with an energy up to 180 J in a duration of 0.5– 0.7 ps at a wavelength of 1:054 m. The laser pulse was focused onto the edge of a supersonic gas jet (2 mm nozzle diameter) using an f=3 off-axis parabolic mirror to a focal spot size of 10 m in vacuum. When helium was used as the working gas, the backing pressure in the gas nozzle was varied to give a plasma density between 0:04–1:4 10 20 cm 3 . The electron density during the interaction was obtained by measuring the plasma fre- quency (! p ) from simultaneous forward Raman scatter- ing measurements. Deuterium gas was also used but at a lower density. The energy spectrum of the ions at 100  from the laser propagation direction was measured with a Thomson parabola ion spectrometer, which enables ions with dif- ferent charge to mass ratio to be distinguished since they produce unique parabolic trajectories at the detector plane. The spectrometer was positioned 80 cm from the VOLUME 93, NUMBER 15 PHYSICAL REVIEW LETTERS week ending 8 OCTOBER 2004 155003-1 0031-9007= 04=93(15)=155003(4)$22.50  2004 The American Physical Society 155003-1