Relativistic laser transparency and propagation in plasma: Is it - PowerPoint PPT Presentation

Relativistic laser transparency and propagation in plasma: Is it governed by dispersion relation or energy balance? Su-Ming Weng Theoretical Quantum Electronics (TQE), Physics Department Technical University of Darmstadt, Germany In collaboration with Prof. Peter Mulser ( TU Darmstadt ) Prof. Hartmut Ruhl ( LMU Munich ) Prof. Zheng-Ming Sheng ( Shanghai Jiaotong University & IoP, CAS ) Prof. Jie Zhang ( Shanghai Jiaotong University & IoP, CAS ) 2-4. May 2011, GSI, Darmstadt, Germany 4th EMMI workshop on Plasma Physics with Intense Heavy Ion and Laser Beams

1 Preface “Open Sesame”, “ Ali baba and the forty thieves ” Who opens the door for relativistic intense laser pulse propagating into an overdense plasma? How does it work?

2 Outline Theoretical background  Classical eletromagnetic (EM) wave propagation  Relativistic induced transparency  Numerical simulations  Relativistic critical density increase  Relativistic laser pulse propagation  Applications  Ion acceleration and Fast ignition  Relativistic plasma shutter  Shortening of laser pulses  Conclusion 

3 Classical EM wave propagation Wave Equation    2    2 0 (in a uniform plasma) E E 2 c Dispersion relation      2 2 2 2 , c k p  plasma frequency is the minimum frequency for EM wave propagation in a plasma. p      2 the electrons will shield the EM field when 4 / e n m p e Critical density     the condition defines the so- called critica l d ensity , n p c    2  2   21   2 3 / 4 1.1 10 / ( [ ]) cm n m e m c e Group velocity (or propagation velocity)  1/ 2 1/ 2    2     1 v n        g  1 p  1       2   c c k n   c

4 Relativistic induced transparency Dimensionless laser amplitude a:     W 2 a     2 2 18 2 1.37 10 μ m I cA   2 2  cm  Single particle’s 8-like motion for a ≥ 1  y y x x-x d a<<1 a ≥ 1 T. C. Pesch and H. – J. Kull, Phys. Plasmas 14, 083103 (2007).

5 Relativistic induced transparency If |v| ~ c,       2 2 1/2 (1 / ) m m v c m 0 0 e e e Relativistic critical density       2 2 / 4 n m e n cr e c the Lorentz factor averaged from the single particle‘s 8-like motion    2 1/ 2 [1 / 2] , the local total field ampl t i ude . a a t t Group velocity (relativistic)  1/2 1/2     v n n     g 1 1          c n n   cr c P. Mulser and D. Bauer, “ High Power Laser-Matter Interaction ” , Springer, 2010.

6 A new diagnostics for determing the critical density Laser and plasma parameters  Cycle-averaged propagation appears very regular,     0, 5 x  laser is mainly reflected at the relativistic critical surface    , 20  n n x max e  the steady state relativistic wave equation is satisfied well    exp ( 20 ) / , otherwise;  n x L max relativistic wave equation:   2 1/2 2 (1 ) , is the scale l en gth. n a L max  2 n     2 (1 ) 0 e E E 2 c n cr   10, incident angle =0 a Incident wave field energy density     2 2 ( ) / 4 ( ) / 4 E E B E B in y z z y Reflected wave field energy den sit y     2 2 ( ) / 4 ( ) / 4 E E B E B re y z z y

7 Critical density VS laser intensity In a normally incident and linearly polarized laser pulse,  a the total field amplitude at critical surface and the incident t    a 2 2 laser amplitude approximately satisfy / 2 1 a a t      2 1/ 2 2 1/ 2 [1 / 2] [1 ] n a n n a n cr t c R c L=3  L (LP) 100 L=  L (LP) n R n cr /n c   if density scale length L 10 n almost of no dependence on L cr 1 0.1 1 10 100 a

8 Effect of laser polarization For circular polarization, a sharp density peak restricts the  critical density increase and prevents the laser propagation    for 10, 0 a (a) Linear polariza tion    2 1/2 =8.96=[1 ] , a c 2 a    0.79 3 t 2 2 a (b) Circular polarization     2 1/2 7.29=[ 1 ] , a c 2 a    0.521 t 2 2 a

9 Effect of laser polarization For normal incident, the relativistic critical density increase     2 1/ 2 =[1 ] , a can be well fitted by c    3 0.79 1.36exp( ) (linear polarization)  a    with   1/ 2  0.48 2.15exp ( ) (circular polarization)  a

10 Effect of plasma density profile For normal incident, if density scale length L > λ ,    /n is almost independent of density profile n c cr c For a very steep and relativistically overdense plasma.    /n is strongly suppressed n c cr c   c is only about 3.9 for 10, a with step- like profile    0, 5 x   n   e 20 , 5  n x c electri c field at the surface  1/2 and skin depth 1/ n e

11 Response time of critical density increase Kinetic energy density,    2 ( 1) m c , E n kin c 0 e For relativistic transparency, can be large r than E E k i n em Skin depth,   1/2 / ( / -1) l n n 0 d cr From energy balance, response time t   / /(1- ) , t l E R I d kin L for n 0 =10n c   15 L t

12 Relativistic laser beam propagation (LP)   linear polarization 0,   10, at t=35 , and a L    0, 5 x   n   e 5 , 5  n x c Theoretically   1/ 2     1 / 0.66c, v v n n c prop g cr but from PIC   (15.5 5)   0.35c, v   prop (35 5) L Previous community attributed the inhibition of the propagation  velocity to the oscillation of the ponderomotive force and hence the oscillation of electron density at the laser front. 1 [1] H. Sakagami, K. Mima, Phys. Rev. E 54, 1870 (1996).

13 Relativistic laser beam propagation (CP) Ponderomotive force for circular polarized laser   m    eE m  2 ˆ ( ) , ( ) / , without oscillatio n f v x x v x  p os os 4 x Theoretically   1/ 2     1 / 0.7c, v v n n c prop g cr but from PIC   (8.0 5)   0.1c. v   prop (35 5) L CP pulse propagates even more slowly than LP pulse. Inhibition of propagation velocity is not attributed to the  oscillation of ponderomotive force.

14 Non-relativistic Relativistic transparency  =1- / behide laser front n n  dielectric function =1- / e cr n n e c  =1- / before laser front n n is constant in plasma e c  response time for n n c cr R  =0 at laser front 0 at laser front R ?  ' ' ' ' ' '  '  ' + = , + , E E E E E E E E E E em kin em kin em em kin em kin em          ' 2 ' 2 2 2 2 ( 1) , (2 / ) / 4, / 2, E n m c E n n n m c a E n m c a kin e e em e cr c e em c e    '  2 2    2 1/2 / 4 ( non-relativistic ), [1 / 2 ] E n m c a a kin e e From energy balance, propagation velocity  2 (1- ) (1- ) R n a v R I   c g v    ' '    2   p + (1 )(1 / 2 ) +2 ( 1) E E R n n n a n em kin e c c e   v v v v p g p g

15 Relativistic propagation velocity  2 (1- ) R n a v  c g v         p 2 (1 )(1 / 2 ) +2 ( 1) R n n n a n e c c e n p are the different heights of density ridge formed before laser front   for 1, and =0 a propagation velocity can be well fitted by   exp( / ) v n n v p p cr g

16 Application (a): Ion acceleration and Fast ignition The Break Out Afterburner is an ion acceleration technique  that may achieve the fast ignition L. Yin et al, Laser Part. Beams 24, 291 (2006), Phys. Plasmas 14, 056706 (2007); J. J. Honrubia et al, Nucl. Fusion 46, L25 (2006), J Phys. Conf. Ser. 244 (2010).

17 Application (a): Ion acceleration and Fast ignition The Break Out Afterburner (BOA) is a robust ion acceleration  mechanism that occurs (> 10 20 W/cm 2 , LP) when a nm-scale target turns relativistically transparent Initially, heating Target expands Target becomes is confined to Skin depth widens relativistically the target front Volumetric heating transparent n e <n cr n e <n c BOA begins relativistic classical transparency transparency L. Yin et al, Laser Part. Beams 24, 291 (2006), Phys. Plasmas 14, 056706 (2007).

18 Application (b): Relativistic plasma shutter A relativistic plasma shutter can remove the pre-pulse  and produce a clean ultrahigh intensity pulse This shutter is classically overdense but relativistically underdense. S. A. Reed et al. , Appl. Phys. Lett. 94, 201117 (2009).