Upload
ross-mulley
View
218
Download
0
Tags:
Embed Size (px)
Citation preview
Bubble regime: condition
€
γemax =a02 /2=γg ≈
ω
ωp
1+a02 /2 /2
€
ω <<ωp
Then electrons can be trapped and move with pulse
a) cτ<λ
b) electron velocity exceeds the laser pulse group velocity
pλp is plasma wavelength
τ Is the pulse length
Zhidkov PRE 2004, Pukhov App Phys 2002
Simulation Parameters:I=10 20
W/cm 2
n=10 cm-3
τ=20 fs
19
: 600*80 simulation box μm2
λ =11 μ mp
DLA electrons
Bubble regime
Contour plots ofelectron density2D PIC in units of [n |e|]cr
wake
wave breaking
accelerating field
laser pulse
Blue:electron density
green: laser fieldRed: longitudinal electric field
Bubble regime
bubbletrapped electrons
DLA
bubble at later time
accelerated electrons
accelerated electrons
pulse erosion
Self Focusing,Channeling
€
ω pe−1 << τ <<ωpi
−1( )
€
eA
mc 2= a(x)(ex ± iey )exp[i(hz −ωt)]
Underdense homogeneous plasmaFixed ions Maxwell’s equations+Equation of motionAssuming
€
∇2a + 1−αn
γ
⎛
⎝ ⎜
⎞
⎠ ⎟a = 0
∇ 2Φ = α (n −1)
γ = 1+ a2
α =n0
1− h2 /k 2
These equations can be solved analytically
in 2D (F. Cattani et al, PRE, 2001).
Complete evacuationPartial electron evacuation
€
a(x) =2 α α −1( ) cosh( ε x)
α cosh2( ε x) −ε
ε = α −1
n = 3(1+ a2) + 21+ a2
α(−α − a2)
nmin = 0
€
xd = −1
α
ad ′ a d1+ ad
2
€
tanad [2α ( 1+ ad
2 −1) − ad2 ]1/ 2
α
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟=
1+ ad2
ad
2α 1+ ad2 −1( ) − ad
2[ ]
1/ 2
half of channel width
Numerical Results
€
density =1019cm−3
maximum laser intensity =1020 w /cm2
spot size = 5μm
pulse duration = 270 fs
Red points correspond toanalytical solution
Greens and blue points correspond tonumerical results
€
×1016 w /cm
€
xdhalf of channel width
€
μm€
Ptotal
Comparison with theoretical results:
channel evacuated of electrons
contour plot of electron density
Plot of electron density vs. y
evacuated channel
Strong electrostatic wake
Ex
Contour plot ofelectron density2D PIC (SP)in units of[n |e|]
cr
Contour plots ofLaser intensity 2D PIC (SP)a in unit of(eE/mωc)
In 2D PIC, data taken from a cut along x in the middle of the box. Laser pulse enters from left and propagates along x.
Laser pulse as it enters the plasma
Laser pulse after propagating 240 micrometers
electron density
Wave-breaking and electron acceleration
€
px
mcAccelerated electrons
electrons in front
€
Ex
€
Ey
n
accelerating field
pulse erosioncavity
25 Mev
d N/ d
E [A
r b. U
nit s
]
Energy in ev
Phase space at time= 1031 fs
After wave-breaking electrons are accelerated and injected into the pulse and the accelerating field.4.8% of total number of electrons are accelerated.
energy of accelerated electrons
time=1395 fs
Theoretical studies and particle-in-cell (PIC) simulations of nonlinear processes related to short pulse laser propagation in underdense plasmas. For the laser power above critical power for relativistic self-focusing in two spatial dimensions PIC simulation results converge to stationary laser filaments. Conditions for the formation of multifilament structures are discussed and demonstrated in simulations for relatively long pulses. For short laser pulses nonlinear propagation at relativistic intensities involves pulse erosion, frequency shift and characteristic steepening at the front of the pulse. Different mechanisms of particle acceleration are described including particle trapping at the front of the pulse, acceleration by the plasma wake fields and by the electromagnetic wave. These processes are simulated and discussed in the context of recent experiments with gas jet targets on the ALLS facility.
Abstract
Relativistic self-focusing, electron acceleration and ultra-short laser pulse propagation in underdense plasmas
Neda Naseri , Paul-Edouard Masson-Laborde , Valery Bychenkov, Wojciech Rozmus , University of Alberta , Lebedev Physics Institute 1 1 2 1 1 2
Filamentation of intense laser beam in plasma By using transversely flat modulated laser pulse, filamentation instability is being studied.
Contour plot ofLaser intensity 2D PIC a in unit of(eE/mωc)
€
density =1×1020cm−3
maximum laser intensity = 5 ×1019 w /cm2
FWHM of laser intensity = 40μm
pulse duration = 300 fs
Wave breaking, acceleration (SP)Contour plot of electron density 2D PIC (SP). The picture on the left shows the wave breaking and the picture on the right shows injected electrons.
injected electronswave breaking
Relativistic self-focusing
Maximum intensity is 3 timesbigger than maximum initial Intensity (SP).
€
Pcr =16.2 ×ncr
nGW
€
Pcr = 0.5TW
P = 7.6TW
P =15.2Pcr
parameters as
SP
Contour plot ofLaser intensity 2D PIC (SP)
Snapshots of laser intensity cross section
Pulse erosion, 1D in hydro
pulse erosion
Pulse Field
Density
Longitudinal Field
Strong steepening of longitudinal field
Relativistic fluid model
( )
( )
( )
22 2 2
20
2
2
20
0
pe et x
e e
e
e
e i
n ac a
c n
n n p
t x m
pm c e
t x x
en Zn
x
ω
γ
γ
γ φ
φε
∂ − ∂ = −
⎛ ⎞∂ ∂+ =⎜ ⎟
∂ ∂ ⎝ ⎠
∂ ∂ ∂+ =
∂ ∂ ∂
∂= −
∂
rr
ur
ur
Model equations in 1D:
Maxwell + Full Hydro + Poisson
Maxwell Equation
Hydro: continuity
+ motion equations
Poisson equation
€
px
mc
d N/ d
E [A
r b. U
nit s
]
Electron energy in ev
Electron energy in ev
180 Mev
Electron energy spectrum Phase space
Threshold power for bubble regimeGordienko, phys plasmas, 2005
Numerical models•Particle-in-cell code MANDOR (1D , 2D): Romanov et al. PRL, 2004•Relativistic cold plasma approximation and Maxwell equations in 1D-limited by the absence of kinetic effects•Standard parameters (SP) - consistent with experimental conditions: pulse duration, τ=30fs, spot size=13μm, intensity, I=4*1018 W/cm2, density, n=5* 1019 cm-3, p-polarized. The experiment carried out at the Advanced Laser Light Source (Z. L. Chen, Y. Y. Tsui, R. Fedosejves) • Homogeneous plasma slab with 40 microns linear ramp in the front. 400-800 microns in length - propagation distance is limited by laser pulse scattering and absorption.
ALLS
bubble
I=4 1018, =30fs, n=5 1019cm-3
I=1020, =20fs, n=1019cm-3
[fs]
P[TW]
€
Pthreshold = 0.03× (τ ( fs)
λ (μm))2 TW
n1 < ne < n2
n1
nc
≈8 ×10−3
P(TW)
n2
nc
≈1.6 × (λ (μm)
τ ( fs))3 P(TW)
•From laser plasma accelerators, quasi monoenergetic 70 – 170 MeV, Mangles et al. Nature 2004, Geddes et al. ibid 2004, Faure et al. ibid 2004.
longitudinal filed DLA electrons
100 Mev
DLA electrons
electrons in front part of bubble
electrons in back of bubbleelectrons in front part of bubble
electrons in back of bubble
Input modulated laser pulse
filaments
Lase
r in
tens
ity (
eE/m
ωc)
Lase
r in
tens
ity (
eE/m
ωc)
filaments
Simulation parameters: