Preparation of the concerned sectors for educational and R&D activities related to the Hungarian ELI project

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1 Preparation of the concerned sectors for educational and R&D activities related to the Hungarian ELI project Ion acceleration in plasmas Lecture 10. Collisionless shock wave acceleration in plasmas pas Dr. Ashutosh Sharma Zoltán Tibai 1

2 Contents 1. Introduction 2. Theoretical Background of Shock Wave Acceleration (SWA) 3. Laser-Plasma Modeling for SWA acceleration of protons 4. Experiment and Results 2

3 Introduction Shock Wave A shock wave can occur in a gas or plasma medium where a discontinuity in the pressure exists that travels faster than the speed of sound in the medium. In laboratory shock waves can be generated with high intensity laserplasma interactions. Shock have a characteristic sharp electric field in the pressure transition region that is oriented in the direction of propagation and is able to reflect, under certain conditions, ions to a maximum of twice the shock velocity. Classic Example: Shock wave formed in air at the front of a jet flying at supersonic speeds. A shock is defined as collisionless if the mean free path between particle collisions is larger than the shock width. 3

4 Theoretical Background on Shock Wave Acceleration Electrostatic shock is typically associated with the excitation of ion acoustic waves (IAW) in plasmas with cold ions and high electron temperatures. As these waves grow, they start trapping particles, reaching high field amplitudes and leading to the formation of a shock wave. If the electrostatic potential energy associated with the shock front is higher than the kinetic energy of upstream ions, there shock waves can reflect the upstream ions to twice the shock velocity acting as an efficient ion accelerator. 4

5 Theoretical Background on Shock Wave Acceleration Steady state electrostatic shock structure as seen from the shock frame. Electrons from the upstream region more freely, while electrons from the downstream region can be either free or trapped. Ions, which flow from upstream to downstream, are slowed down by the electrostatic potential, and reflected back into the upstream for strong shocks. 5

6 Theoretical Background on Shock Wave Acceleration (10.1) (10.2) 6

7 Theoretical Background on Shock Wave Acceleration 7

8 Theoretical Background on Shock Wave Acceleration and (10.3) 8

9 Theoretical Background on Shock Wave Acceleration (10.4) (10.5) 9

10 Theoretical Background on Shock Wave Acceleration (10.6) (10.7) 10

11 Theoretical Background on Shock Wave Acceleration (10.8) (10.9) 11

12 Theoretical Background on Shock Wave Acceleration Fig 10.2.a: The upper arrow describes the trajectory of the pseudo-particle which is reflected at the right and returns. The lower arrows show the motion of a pseudo-particle that has lost its energy and is trapped in the potential well. Fig 10.2.b: Trajectory of a soliton 12

13 Theoretical Background on Shock Wave Acceleration and (10.10) 13

14 Theoretical Background on Shock Wave Acceleration and (10.11) 14

15 Theoretical Background on Shock Wave Acceleration Fig 10.3.b: Symmetric reflection and transmission i of particles from soliton. 15

16 Theoretical Background on Shock Wave Acceleration (10.15) 15) (10.16) 16

17 Theoretical Background on Shock Wave Acceleration and approx. 17

18 Theoretical Background on Shock Wave Acceleration Fig b 18

19 Laser-driven Electrostatic collisionless shock wave and ion acceleration 19

20 Laser-driven Electrostatic collisionless shock wave and ion acceleration 20

21 Laser-driven Electrostatic collisionless shock wave and ion acceleration 21

22 Laser-driven Electrostatic collisionless shock wave and ion acceleration As the shock structure overtakes the plasma ions, they are reflected off it and gain a velocity corresponding to twice the shock velocity minus their expansion velocity. Thus reflected ions forms an ion beam that retains its narrow energy spread as it exits the plasma. 22

23 Recent Experiment and Results Experiment: Fig. a. Haberberger, Nat. Phys. 8, 95 (2012) Fig. b. Fig. c. 23

24 Simulation results: Recent Experiment and Results Fig. e. Fig. d. 24 Nat. Phys. 8, 95 (2012)

25 Simulation Results CO 2 Laser Pulse (circularly polarized) Interaction with Underdense H 2 Plasma electrons (in black) are accelerating behind the laser pulse (in green). 25

26 Simulation Results CO 2 Laser Pulse (linearly polarized) Interaction with overdense H 2 Plasma Proton Acceleration via SWA mechanism. Laser Field Target: H 2 Plasma Electron Momentum Distribution Ion Momentum Distribution Shock Wave Field 26

27 Simulation Results CO 2 Laser Pulse (linearly polarized) Interaction with overdense H 2 Plasma Proton Spectrum via SWA mechanism. 27

28 Problems Q10.1. Q10.1. Q10.2. A10.2. Q10.3. A10.3. True of False. A shock wave is a disturbance that propagates through a medium faster than the speed of light. False. What is the difference between collisional andcollisionless shock wave? Collisionless Shock - means free path between particle collisions i > shock width. Collisional i l Shock - means free path between particle collisions < shock width. Write down the shock velocity of collisionless shock. M c s, M (>1) is the Mach number and c s is the ion sound speed. 28

29 Problems Q10.4. A10.4. True or False. Shock wave have a characteristic sharp electric field in the pressure transition region that is oriented in the direction of propagation and is able to reflect, under certain conditions, ions to more than twice the shock velocity. False. Q10.5. What is the origin of electrostatic shock wave. A10.5. Shock waves are typically associated with the excitation i of fion acoustic waves (IAW) in plasmas with cold ions and high electron temperatures. As these waves grow, they start trapping particles, reaching high field amplitudes and leading to the formation of a shock wave. Q10.6. What is critical value of Mach number for the existence of shock wave. A

30 Problems Q10.7. A10.7. Q10.8. A10.8. Explain in brief the mechanism of laser driven shock wave generation in plasma. The interaction of super-intense laser pulses with overdense plasma, the light pressure ranges from gigabar to terabar values and, like a piston, may sweep out and compress the laser produced plasma and push its surface at nearly relativistic speeds. Such combination of strong compression and acceleration is the origin for generation of strong collisionless shock waves. Why ion acceleration by collisionless shock is more interesting? Monoenergetic energy spectrum of the accelerated ions. Q10.9. Why ion acceleration by collisionless shocks in the target bulk is more prominent in case of linearly polarized pulses? A10.9. The oscillating component of the v B drives a sweeping oscillation at 2ω of the density profile which overlaps to the steady effect of the ponderomotive force and causes strong absorption and fast electron generation. 30

31 Problems Q A Explain in brief the recent experiment finding on laser driven collisionless shock wave acceleration (CSA) of protons. CSA has been indicated as the mechanism responsible for monoenergetic acceleration of protons up to 22 MeV in the interaction of CO 2 laser pulses (wavelength 10μm) μ with hydrogen gas jets at intensities up to Wcm 2. The particular temporal structure of the laser pulse, i.e., a 100 ps train of 3 ps pulses, was found to be essential for the acceleration mechanism, since no spectral peaks were observed for a smooth, not modulated pulse. 31

32 References 1. F. F. Chen, Introduction to Plasma Physics, (Plenum Press, New York, 1974). 2. S. Eliezer, The Interaction of High-Power Lasers with Plasmas, (IOP Publishing, Bristol, 2002). 3. W. L. Kruer, The Physics of Laser Plasma Interactions, (Addison-Wesley Publishing Company, California, 1988). 4. P. Gibbon, Short Pulse Laser Interaction with Matter, (Imperial College Press, 2005). 5. Macchi et.al., Review of fmodern Physics 85, 751 (2013). 6. D. A. Tidman and N. A. Krall, Shock Waves in Collisionless Plasma, (Wiley Interscience, 1971). 32