Transcript Rational paradigm of plasma Physics

A decay of electromagnetic wave
quanta in a turbulent plasma
during their interaction with
Langmuir waves
a,b
IA&E SB RAS
EROFEEV Vasily
a,c
MESHCHERIAKOV Dmitry
a) Laboratory of nonlinear physics
Institute of Automation and Electometry
Siberian Branch of Russian Academy
of Sciences
b) Novosibirsk State University
Physical Department
c) Novosibirsk State University
Department of Information Technologies
A key objective of developing natural sciences
consists in heightening the information content of
conclusions regarding phenomena in
surrounding world.
The progress of theoretical physics in XX-th
century has complied with this objective
insufficiently well.
An impressive illustration to this statement has
been worked out by the plasma studies:
Traditional concepts of nonlinear plasma
theory cannot provide appropriate level of
reliability of final predictions.
(An Informativeness of plasma physical
scenarios is unacceptable low.)
The problem of wave quanta decay
 Traditional viewpoint: Nonlinear phenomena in weakly
turbulent plasmas conserve the total number of
Langmuir wave quanta
̶
A.S Kompaneyets, Zh. Eksp. Teor. Fiz. 31, 876 (1956).
– L. M. Gorbunov, V. P. Silin, Sov. Phys. JETP 20, 135 (1965).
– V.N. Tsytovich, Sov. Phys. Uspekhi 15, 632 (1973)
 Alternative opinion: Langmuir waves quickly transmit
their energy to bulk plasma electrons during a stochastic
electron acceleration
– F.G. Bass, Ya.B. Fainberg and V.D. Shapiro, Sov. Phys. JETP 22,
230 (1966).
First reason of theory non-informativeness:
The ENSEMBLE METHOD (substitution of
real plasmas by plasma ensembles)
“Incarnations” of the ensemble method in
plasma theory:
 BBGKY plasma kinetics
 Hydrodynamic modelling of nonlinear plasma
phenomena
 Wave phase averaging
 Hamiltonian approaches to description of
phenomena in a turbulent plasma
 …
The picture of ensemble evolution strongly
depends on the ensemble content:
Differing ensembles exhibit diverging
interference of their evolving statistic.
A general practice in physical theorizing was to
regard particular deductions on the interference
of the ensemble statistics as a genuine laws of
the system physical evolution.
Information-theoretical aspect of
plasma description:
Absence of full data on particle positions and
momentums
Impossibility to predict plasma behavior
during infinite time period
The main goal: to develop reliable scenario of plasma
evolution for as a longer period as possible
Careful separation of informational basis of the theory
from full (never known!) plasma information
Noncompliance of plasma ensemble
substitutions with above principle
Second reason of theory noninformativeness:
AN ASYMPTOTIC CONVERGENCE OF
SUCCESSIVE ITERATIONS
 Dependence of final deductions regarding the
physical laws of the plasma evolution on the
lowest order approximation of the perturbation
theory. Necessity of selecting the most rational
choice of the lowest order approximation:
̶
First successive iterations of nonlinear perturbation
expansion converge to conditional limit that depends
on the theory leading order
̶ Differing conditional limits stands for varying
scenarios of the plasma evolution
Second reason of theory noninformativeness:
AN ASYMPTOTIC CONVERGENCE OF
SUCCESSIVE ITERATIONS (slide 2)
 Restrictions on appropriateness of certain
mathematical procedures in intermediate calculations:
Fourier and Laplace transformations are fraught with
deviation of final theoretical deductions from objective
physics of plasma evolution:
̶
In computing scenario of plasma evolution, one should use
predominantly the data on current plasma state and on its
relatively recent past
̶
Temporal Forier and Laplace transforms do not discriminate
data on plasma states at remote periods of time
Two earlier reasons of theory noninformativeness cannot be separated:
̶ Had the picture of ensemble evolution not
depended on the ensemble content, one may
have substantiated by ensemble variations the
diversity of lowest order approximations.
̶ Variations of lowest order approximation within
the practice of ensemble studies suppose
appeals to differing ensembles; absence of
dependence of plasma evolution picture on the
theory leading order would have meant then the
independence of the picture of the ensemble
evolution on the ensemble content.
• It is necessary to gain existing practice of
•
•
physical theorizing by creating new approaches
that both refrain from traditional plasma
ensemble substitutions and take proper account
of the asymptotic nature of successive iterations.
An approach of this type, The correlation
analysis of plasma kinetics, is created for
studies of turbulent plasma phenomena.
The revealing of other plasma contexts yielding
any informative final theoretical conclusions and
the developing of theoretical means for inferring
respective conclusions should constitute an
extremely important component of further
plasma research.
Principles of getting high-informative
plasma kinetic scenarios: A REFRAIN FROM
THE PLASMA ENSEMBLE SUBSTITUTION
With refraining from the the plasma ensemble
averaging, one is forced to substitute the latter by a
contextually oriented averaging in phase space of
plasma particles. Particularly, the statistic of
distribution function is defined as a density of particles
within voluminous areas of  -space:
f   N  ( r , p, t )

Principles of getting high-informative
plasma kinetic scenarios: A DIRECT TIME
INTEGRATION OF INTERMEDIATE
EVOLUTION EQUATIONS
The direct time integration discriminates the
indeterminate data on time remote plasma states
via the “phase mixing” within corresponding
nonlinear integrals
̶
Comments on top informativeness
of final theoretical deductions
The possibility of developing informative conclusions depends
essentially on the theory expansion parameter. With expansion
parameter , the most optimal order of the expansion is about 1 / .
Up to this top level, the adding of extra orders leads to enlarging the
time interval of reliability of respective plasma scenario. In the
plasma turbulence case, the expansion parameter is
the ratio of typical wave damping rate  to the width of
turbulence spectrum in natural frequencies   , then conclusions
on current plasma evolution up to n -th order are reliable up to time
delays of the order of


̶
() n1 /  n .
Presumably, in other cases the expansion parameter should also
constitute a ratio of two characteristic inverse times, with analogous
estimation of the period of the scenario reliability.
Thermalization of electromagnetic wave
quanta in a turbulent plasma
The rate of wave
energy dissipation:

Here
Nk
, 



 k ~   nl 
k Nk
3 S t N
k


2 

is the quanta density of electromagnetic waves with polarization
is the natural frequency of the wave,
k
components of wave collision integral
 knl

  pe 
  
 k 
2
~
S t Nk
and
 Nk
nl
k
are the
StNk :
 N k
 StN k  S~t N   2 knl N k
k
t
,
is the nonlinear wave damping rate.
Comment: Total wave energy in the unit of plasma volume is given by
integral
d 3k  N 
 (2 )3 k k
Beam-plasma experiments
 Wong et al.:
̶
̶
A.Y. Wong and P.Y. Cheung, Phys. Rev. Lett. 52, 1222 (1984).
P.Y. Cheung and A.Y. Wong, Phys. Rev. Lett. 55, 1880 (1985).
M.D. McFarland and A.Y. Wong, Phys. Plasmas 4, 945 (1997).
M.D. McFarland and A.Y. Wong, Phys. Rev. Lett. 84, 666 (2000).
̶
̶
 Vyacheslavov et al:
̶
̶
L.N. Vyacheslavov et al.,
Proc. of the IV-th International Workshop “Strong Microwaves in
Plasmas,” Nizhny Novgorod, Inst. of Applied Physics, 1999, ed. A.G.
Litvak (Nauka, Moscow, 2000) Vol. 2, p. 405
L.N. Vyacheslavov et al., JETP Letters 75, 41 (2002).
L.N. Vyacheslavov et al., PPCF 44, B279 (2002).
̶
̶
 Benford et al:
– D. Levron, G. Benford and D. Tzach, Phys. Rev. Lett. 58, 1336 (1987).
– G. Benford, X. Zhai and D. Levron, Phys. Fluids B 3, 560 (1991).
– G. Benford and X.L. Zhai, Phys. Fluids B 5, 1914 (1993).
Reduction of full plasma description
Full plasma description = Klimontovich-Dupree
equation + Maxwell equations
Microdistribution (Klimontovich):
N (r , p, t )   (r  ri (t )) ( p  pi (t ))
3
3
i
The microdistribution cannot be rendered as a
constructive notion of the theory: it depends
essentially on the positions and momenta of all
plasma particles.
f   N  ( r , p, t )
Distribution function:
An infinite hierarchy of evolution equations for
multipoint correlation functions:
̶
Distribution function
correlation function
f
is advanced in time by the two-point
N E  ( R, p, t , t ) 
N (r , p, t ) E (r  R, t ) ,
The two-point correlation function is advanced in time by the three̶
point correlation function
NEE ( R, R, p, t, t, t)
 N (t ) E(r  R, t)  E(r  R, t) .
̶
…
̶
After the hierarchy truncation at a reasonable order, the
system can be reduced to simultaneous evolution equations of
distribution function and two-point correlation function
The case of a plasma with weak
Langmuir turbulence: logics of obtaining
simplified kinetic description
The characteristic time of plasma and spectrum evolution, T   , is
great compared to inverse spectrum width in natural frequences  .1
In collision integral of plasma particles, the effect of two-point
correlation function can be expressed in terms of the two-time
1
̶
̶
correlation function
E (r , t )  E (r  R, t )
̶
The two-point correlation function drives via Maxwell equations the
two-time correlation function
̶
Within domain    t  t   , the evolution equation of twotime correlation function can be directly integrated: the function can be
expressed in terms of wave spectral density nk (t ).
̶
The resulting expression (of the two-time correlation function) can be
used for obtaining time derivatives of distribution functions and spectral
density
1
1