How much laser power can propagate through fusion plasma? Pavel Lushnikov 1,2,3 and Harvey A. Rose 3 1 Landau Institute for Theoretical Physics 2 Department of Mathematics, University of Notre Dame 3 Theoretical Division, Los Alamos National Laboratory
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How much laser power can propagate through fusion plasma? Pavel Lushnikov 1,2,3 and Harvey A. Rose 3 1 Landau Institute for Theoretical Physics 2 Department.
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How much laser power can propagate through fusion plasma?
Pavel Lushnikov1,2,3 and Harvey A. Rose3
1Landau Institute for Theoretical Physics 2Department of Mathematics, University of Notre Dame 3Theoretical Division, Los Alamos National Laboratory
Even for very small correlation time, ,there is forward stimulated Brillouin instability
- light
- ion acoustic wave
Numerical confirmation: Intensity fluctuations power spectrum1
/ kmcs
k /
km
- acoustic resonance1P. M. Lushnikov, and H.A. Rose, Phys. Rev. Lett. 92, p. 255003 (2004).
Instability for
Random phase plate:
Wigner distribution function:
Eq: in terms of Wigner distribution function:
Boundary conditions:
Equation for density:
Fourier transform:
-closed Eq. for Wigner distribution function
Linearization:
Dispersion relation:
Top hat:
Instability growth rate:
2 2
0 204
e
c e e
nF I eI
n m T
Maximum of instability growth rate:
- close to resonance
and depend only on : 2 2
0 204
e
c e e
nF I eI
n m T
Absolute versus convective instability:
is real : convective instability only.
There is no exponential growth of perturbations in time – only with z.
Density response function:
- self energy
As
Pole of corresponds to dispersion relation above.
Collective stimulated Brillouin instability Versus instability of coherent beam:
- coherent beam instability
- incoherent beam instability
Instability criteria for collective Brillouin scattering
-convective growth rate
perturbations ~
Instability is controlled by the single parameter:
I 1
F2 ne
nc
vosc
ve
2
1
Pspeckle
Pcritical
2 2
0 204
e
c e e
nF I eI
n m T - dimensionless laser
intensity
- Landau damping
F - optic f-number
Comparison of theoretical prediction with experiment
* 2 /i i i ii i
Z n Z n Z -effective plasma ionization number
in - number density for I-th ion species
iZ - ionization number for I-th ion species
Solid black curve – instabilitythreshold
~2keVeT14 2
0 1.5 10 W/cmI
Second theoretical prediction:
Threshold for laser intensity propagation does not depend oncorrelation time for cT 1.s c cc l T
=3.4pscT
=1.7pscT
10.2pss cc l
National Ignition Facility for He-H plasma
~5keVeT
* 1.7Z Thermal effects are negligible in contrast with Rochester experiments
15 20 2x10 W/cmI
By accident(?) the parameters of the original NIF design correspond to the instability threshold
NIF:
Theoretical prediction for newly (2005) proposedNIF design of hohlraum with SiO2 foam:
~5 keVeT
He is added to a background SiO2 plasma, in order to increase the value of
and hence the beam spray onset intensity.
15 -10/ 0.1, 8, 5.4 10 sece cn n F
Fluctuations are almost Gaussian below threshold:
And they have non-Gaussian tails well above FSBS instability threshold:
Below threshold a quasi-equilibrium is attained:
True equilibrium can not be attained because slowly grows with z for any nonzero Tc:
Slope of growth can be found using a variantof weak turbulence theory:
Linear solution oscillate:
But is a slow function of z
Boundary value:
For small but finite correlation time, ,kinetic Eq. for Fk is given, after averaging over fastrandom temporal variations, by:
Solution of kinetic Eq. for small z:
which is in agreement with numerical calculation of
depends strongly on spectral formof , e.g. for Gaussan value of is about 3 times larger.
Change of spectrum of with propagation distance is responsible for change of the slope :
Growth of is responsible for deviationof beam propagation from the geometricaloptics approximation which could be critical for the target radiation symmetry in fusion experiments.
Intermediate regime near the threshold of FSBS instability
Electric field fluctuations are still almost Gaussian:
But grows very fast due to FSBS instability:
Key idea: in intermediate regime laser correlation length rapidly decreases with propagation distance:
Laser beam
Backscattered light
Plasma
and backscatter is suppressed due to decrease ofcorrelation length1
1H. A. Rose and D. F. DuBois, Phys. Rev. Lett. 72, 2883 (1994).
Light intensity:
Laser intensityinnintensityinte
Dopant concentration
Weak regime Intermediate regime Strong regime
Geometric optics Ray diffusion Beam spray
For example: 1% Xe added to He plasma, with temperature 5keV, ne/nc= 0.1, Lc=3m, 1/3m light, induces transition between weak and
intermediate regime for 70% of intensity compare with no dopant case.
Small amount (~ 1%) of high ionization state dopant may lead to significant thermal response, T, because
Result: change of threshold of FSBS due toChange in effective , and, respectively, changeOf threshold for backscatter.
April-May 2006: new experiments of LANL teamat Rochester: very high stimulated Raman scattering
- light
- Langmuir wave
Theoretical prediction: beam spray vs. stimulated Raman scattering
SRS intensity amplification in single hot spot
Probability density for hot spot intensity
Average amplification diverges
for
- amplification factor
Leads to enhanced (but not excessive) beam spray,
Add high Z dopant to increase thermal component of plasma response
Causing rapid decrease of laser correlation lengthwith beam propagation1
Raise backscatter intensity threshold2
Diminished backscatter
How to control beam propagation
2H. A. Rose and D. F. DuBois, PRL 72, 2883 (1994).1P. M. Lushnikov and H. A. Rose, PRL 92 , 255003 (2004).
Conclusion
Analytic theory of the forward stimulated Brillouin scattering (FSBS) instability of a spatially and temporally incoherent laser beam is developed. Significant self-focusing is possible even for very small correlation time.
In the stable regime, an analytic expression for the angular diffusion coefficient, , is obtained, which provides an essential corrections to a geometric optics approximations.
Decrease of correlation length near threshold of FSBScould be critical for backscatter instability and future operations of the National Ignition Facility.