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

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

Relativistic laser transparency and propagation in plasma: Is it governed by dispersion relation or energy balance?

1

Preface

“Open Sesame”, “Ali baba and the forty thieves” Who opens the door for relativistic intense laser pulse propagating into an

• verdense 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



Dispersion relation

2 2 2 2, p

c k    

the condition defines the critica so- l d called ensity ,

p c

n   

2 2 21 2 3

/ 4 1.1 10 / ( [ ]) cm

c e

n m e m    



  



Group velocity (or propagation velocity)

1/ 2 1/ 2 2 2

1 1 1

g p c

v n c c k n                          

2

plasma frequency is the minimum frequency for EM wave propagation in a plasma. the electrons will shield the EM field when 4 /

p p e

e n m      



Critical density



Wave Equation

2 2 2

0 (in a uniform plasma) c      E E

4

Relativistic induced transparency



Single particle’s 8-like motion for a ≥ 1

x y

a<<1

x-xd y

a

≥1

• T. C. Pesch and H. –J. Kull, Phys. Plasmas 14, 083103 (2007).

2 2 18 2 2

W 2 1.37 10 μm 2 cm I cA

a

          



Dimensionless laser amplitude a:

5

Relativistic induced transparency



If |v| ~ c,

2 2 1/2

(1 / )

e e e

m m v c m 



  

2 1/ 2

[1 / 2] , the local total field ampl t . i ude

t t

a a   

2 2

/ 4

cr e c

n m e n     



Group velocity (relativistic)

1/2 1/2

1 1

g cr c

v n n c n n                   



Relativistic critical density the Lorentz factor averaged from the single particle‘s 8-like motion

• P. Mulser and D. Bauer, “High Power Laser-Matter Interaction”, Springer, 2010.

6

A new diagnostics for determing the critical density

 

max max 2 1/2 max

0, 5 , is the scale l 20 exp ( 20 en ) / , otherwise; 2 gth. (1 ) ,

e

x n n x n x L n L a             



Laser and plasma parameters



Cycle-averaged propagation appears very regular, laser is mainly reflected at the relativistic critical surface the steady state relativistic wave equation is satisfied well

10, incident angle =0 a  

2 2 2 2

Incident wave field energy density Reflected wave field energy den ( ) / 4 ( ) / sit 4 ( ) / 4 ( ) / 4 y

in y z z y re y z z y

E E B E B E E B E B        

2 2 2

relativistic wave equation: (1 )

e cr

n c n      E E

7

Critical density VS laser intensity

0.1 1 10 100 1 10 100

L=3 L (LP) L=  L (LP) nR

ncr/nc a

cr

if density scale length n almost of no dependence on L L  

2 1/ 2 2 1/ 2

[1 / 2] [1 ]

cr t c R c

n a n n a n     



In a normally incident and linearly polarized laser pulse, the total field amplitude at critical surface and the incident laser amplitude approximately satisfy

t

a

2 2

/ 2 1

t

a a    a

8

Effect of laser polarization

for 10, a   



For circular polarization, a sharp density peak restricts the critical density increase and prevents the laser propagation

2 1/2 2 2

=8.96=[1 (a) Linear polariza ] , 0.79 2 tion 3

c t

a a a      

2 1/2 2 2

7.29=[ (b) Circular 1 ] , 0.521 polarization 2

c t

a a a       

9

Effect of laser polarization



For normal incident, the relativistic critical density increase can be well fitted by

3 1/ 2

0.79 1.36exp( ) with 0.48 2.15exp (linear polarization) (circular polarization) ( ) a a           

2 1/ 2

=[1 ] ,

c

a   

10

Effect of plasma density profile



For a very steep and relativistically overdense plasma.



For normal incident, if density scale length L>λ,

c

/n is almost independent of density profile

cr c

n  

c

/n is strongly suppressed

cr c

n  

1/2

electri with step- c field at like profile 0, the surface and skin depth 1/ 5 20 , 5

e c e

n n n x x         

c is only about 3.9 for

10, a  

11

Response time of critical density increase

From energy balance, response time t Kinetic energy density,

15 L t  

1/2

/ ( /

• 1)

d cr

l n n  

k 2 kin c n e i em

For relativistic transparency, can be large ( 1) m c , r than E n E E   

Skin depth,

d kin

/ /(1- ) ,

L

t l E R I  

for n0 =10nc

12

Relativistic laser beam propagation (LP)



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

L

linear polarization 0, 10, at t=35 , and 0, 5 5 , 5

e c

a x n n x            

 

1/ 2

Theoretically 1 / 0.66c, but from PIC (15.5 5) 0.35c, (35 5)

prop g cr prop L

v v n n c v          

[1] H. Sakagami, K. Mima, Phys. Rev. E 54, 1870 (1996).

13

Relativistic laser beam propagation (CP)



Inhibition of propagation velocity is not attributed to the

• scillation of ponderomotive force.

2

ˆ ( ) , without oscillatio ( ) / 4 n ,

• s

p

• s

v x m f v x x x eE m     

 

1/ 2

Theoretically 1 / 0.7c, but from PIC (8.0 5) 0.1c. (35 5)

prop g cr prop L

v v n n c v          



Ponderomotive force for circular polarized laser

CP pulse propagates even more slowly than LP pulse.

14

Non-relativistic Relativistic transparency

dielectric function =1- / is constant in plasma

e c

n n  =1- / behide laser front =1- / before laser front response time for

e cr e c c cr

n n n n n n   

' ' ' '

+ = ,

em kin em kin em

E E E E E 

' ' ' '

+ ,

em kin em kin em

E E E E E  

' 2 ' 2 2 2 2 ' 2 2 2 1/2

( 1) , (2 / ) / 4, / 2, / 4 ( ), [1 / 2 non-relativistic ]

kin e e em e cr c e em c e kin e e

E n m c E n n n m c a E n m c a E n m c a a                

?

=0 at laser front R 0 at laser front R 

2 ' ' 2

(1- ) (1- ) + (1 )(1 / 2 ) +2 ( 1)

c g p em kin e c c e

R n a v R I v E E R n n n a n           

From energy balance, propagation velocity

p g

v v 

p g

v v 

15

Relativistic propagation velocity

propagation velocity can be well fitted by exp( / ) for 1, and =0

p p cr g

v a n n v    

np are the different heights of density ridge formed before laser front

2 2

(1- ) (1 )(1 / 2 ) +2 ( 1)

c g p e c c e

R n a v v R n n n a n          

16

Application (a): Ion acceleration and 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).



The Break Out Afterburner is an ion acceleration technique that may achieve the fast ignition

17

Application (a): Ion acceleration and Fast ignition



The Break Out Afterburner (BOA) is a robust ion acceleration mechanism that occurs (> 1020 W/cm2, LP) when a nm-scale target turns relativistically transparent

Initially, heating is confined to the target front Target expands Skin depth widens Volumetric heating Target becomes relativistically transparent BOA begins

ne <ncr

relativistic transparency

ne <nc

classical 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

• S. A. Reed et al., Appl. Phys. Lett. 94, 201117 (2009).

This shutter is classically overdense but relativistically underdense.

19

Application (c): Shortening of laser pulses



A quasi-single-cycle relativistic pulse can be produced by ultrahigh laser-foil interaction

• L. L. Ji et al., Phys. Rev. Lett. 103, 215005 (2009).

The thin foil initially is relativistically

• verdense.

When it evolves into a thick but rare plasma, it becomes relativistically transparent.

20

Conclusion



Relativistic induced transpancy makes the propagation of a relativistic laser pulse into an overdense plasma possible

• We clarify the underlying physics of the relativistic critical density increase, and

propose a method for determining the relativistic critical surface and the relativistic critical density increase.

• We have shown that the critical density increase strongly depends on the plasma

density profile and laser polarization, and have discovered and explained a rather long response time for the relativistic critical density increase.



Relativistic laser pulse propagation is governed by energy balance

• The propagation velocity is much less than the group velocity from dispersion relation

when the total energy density in plasma exceeds the wave energy density in vacuum.



The relativistic induced transparency finds wide applications in fast ignition scheme, ion acceleration, relativistic plasma shutter, and shortening of laser pulses.

Thanks for your attention!