Transcript Observations of non-resonant scattering from the sea

Detection of forecoming bifurcations in
plasma on the basis of prebifurcation noise
enhancement phenomenon (project 2.1)
Research group:
Prof. S. Berczynski, Szczecin University of Technology
Prof.. Yu.A.Kravtsov, Maritime University of Szczecin
Dr. habil. Elena Surovyatkina, Space Research Institute, Russ.
Acad.Sci., Moscow
Potential partners:
Ph. Ghendrih and X. Garbet,, France, CEA and
L. Villard, Switzerland.
• The concept of the NOISE PRECURSOR for
forecomig bifurcations was introduced first by
Wiesenfeld (1996). The linear theory of
Wiesenfeld predicts the infinite growth of
fluctuations near bifurcation threshold.
Nonlinear theory was developed by the joint
efforts of MUS, SUT and Space Research Institute
(Moscow). Nonlinear theory implies
SATURATION FOR FLUCTUATIONS
GROWTH near the bifurcation threshold and
thereby makes the problem of bifurcation
prediction more realistic.
Example: bifurcation of period
doubling in the nonlinear map
Map:
xn 1
xn1  F ( xn )  noise
T=1
xn
T=2
xn
Bifurcation Diagram
Bifurcation diagram
x
Linear teoria
by Wiesenfel
(unlimited growth of
fluctuations)
Nonlinear
saturation
Rysunek
Control parameter

Bifurcation of the symmetry breaking in the
nonlinear oscillator
• Equation for nonlinear oscillator:
d 2x
dx U ( x, t )
 2

  (t )
2
dt
dt
x
U ( x, t )  A(t ) x 2  B(t ) x 4
B<0
B>0
albo
Bifurcations, which take place in a hot plasma
(information from Dr. L. Villard, Switzerland.)
• ELM sequences,
• L-H transitions,
• NTM hysteresis,
• Equilibrium bifurcations.
Practical problem: lack of funds for trips to the
Euratom Research Centers to initiate the joint
studies of the experimental materials on
bifurcations.
(Fresh example: Invitation from Dr.Ph. Ghendrih,
Cardache, to participate in „Pedestal” conference
in France, 4-6 April 2006)
• Publications
• 1. Kravtsov Yu.A., Belchinskaia S.G., Butkovskii O.Ya., Rychka I.A.,
Surovyatkina E.D. Prebifurcational noise rise in nonlinear systems. JETP, 2001,
93(6), 1323-1329.
• 2. Yu.A. Kravtsov, E.D.Surovyatkina. Nonlinear saturation of prebifurcation
noise amplification. Phys. Lett. A, 2003, 319(3-4), 348-351.
• 3. E.D.Surovyatkina. Rise and saturation of the correlation time near
bifurcation threshold. Phys. Lett. A, 2004, 323(2), 128-134.
• 4. Yu.A.Kravtsov, S.G.Bilchinskaia, I.A.Rychka, E.D.Surovyatkina.
Phenomenon of prebifurcation noise enhancement as diagnostic instrument for
plasma systems, influenced by external noise. Plasma-2003, CBK PAN,
Warszawa, 8-12 Sept. 2003
• 5. S.Berczyński, Yu.A.Kravtsov, E.D.Surovyatkina. Fluctuations enhancement
ar a precursor of bifurcations in nonlinear systems. VIII School of Modal
Analysis, AGH, Kraków, 1-2 Dec. 2003, pp. 7-12.
• 6.Surovyatkina E.D., Kravtsov Yu.A., Kurths J. Fluctuation growth and
saturation in nonlinear oscillator on the threshold of bifurcation. Phys. Rev. E,
2005, 72(4), 046125, pp.1-7.