T10 l Circular crosssection l R 1 5

T-10 токамак l. Circular cross-section l. R = 1. 5 m a. L = 0. 3 m l. BT 3 T l. IP 500 k. A lt ~ 1 sec ln 6 x 1013 cm-3 ECRH system up to 1. 8 MW, t = 0. 4 sec 4 gyrotrons at 140 GHz 1 gyrotron at 130 GHz

HYBTOK-II токамак Nagoya University l. Circular cross- section l. R = 0. 4 m a. L = 0. 11 m l. BT 0. 3 T l. IP 5 k. A lt ~ 0. 15 sec ln 2 x 1012 cm-3

Linear Plasma Device, NAGDIS-II 0. 3 m linear divertor plasma simulator , n~1020 m-3 in steady state. Detached plasma condition by increasing neutral gas pressure

Large Helical Device LHD superconducting heliotrontype device with a set of l = 2/m = 10 R = 3. 9 m, a = 0. 65 m, Bt < 2. 89 T, NBI power, PNBI < 5 MW, ne < 8 × 1019 m − 3 - 1. 5 × 1020 m− 3 Te < 4. 4 ke. V , Ti < 3. 5 ke. V t. E~ 0. 3 s LHD Divertor probes • l=1 mm • d=6 mm • f=250 k. Hz

Interball , 1998 Interball-1 500 - 200000 km, Interball-2 500 -20000 km

Interball-1 OT summary In summer outer cusp throat (OT) is open for the MSH flow. TBL (turbulent boundary layer) is mostly in MSH. In winter OT is closed by smooth MP at larger distance. Inside MP ‘plasma balls’ (~few Re) contain reduced field, heated plasma & weaker TBL. OT encounters on 98. 06. 19 at 10 -11 UT by Interball-1 and Polar are shown

Параметры плазмы T-10 HYBTOK-II NAGDIS-II Earth’s magnetopause Magnetic field, T ~2 ~0. 3 ~0. 1 (1 -10)*10 -9 Core plasma density , cm – 3 6 1013 3 1012 ~1014 Core plasma electron temperature, e. V ~2000 ~200 ~10 Edge plasma density , cm – 3 ~3 1012 ~1 1012 ~3 1012 ~1 -100 Edge plasma electron temperature, e. V ~10 -50 ~1 -3 ~20 Edge plasma ion temperature, e. V ~10 ~2 -5 <1 ~7 Plasma scale, m ~1 ~0. 2 ~0. 1 ~108

Функция распределения (PDF) For fully random fluctuation (Kolmogorov-type model ) PDF is a Gaussian Coherent events: deviation from a Gaussian ( reduce the number of degrees of freedom , process called as intermittent) close to Gaussian PDF Intermittent bursts Large amplitudes exhibit non-Gaussianity.

3 D isotropic MHD turbulence, DNS Biskamp Mueller small-scale turbulent structures: Current-density isosurfaces vorticity isosurfaces

Каскадные процессы: мультипликативные модели ln=2 -n. L, ln. X(t)= ( i=1 -n. Wi) LX(t) E 1/2 E 1 -1/p E Single exponent (dimension) 1/p. E Family of exponent (spectrum of dimensions) Monofractal isotropic process: Kolmogorov type Multifractal process: long-range correlations, memory effect Rather considerable generalization of fractal geometry

Наблюдение мультифрактальности (многомасштабности) PDF of increments l. X(t)=X(t+l)-X(t), depends on scale, l=1 -128 mcs Coarse integral time T~50 -200 s

Brownian motion does not demonstrate multifractality: monofractal, trivial self-similarity l, lag PDF’s of increments l. X(t)=X(t+l)-X(t), don’t depend on scales l

Cascading in log-Poisson model of intermittency: random multiplicative process Coherent structure of large scale defects Random multiplicative process: energy dissipation rate ε at two different scales l 1 and l 2: ε(l 2)=W(l 1, l 2) ε(l 1) ε(l)~lτ(q) , log(Wq(l 1, l 2) )/log(l 2/l 1)=τ(q) The defects adds a finite amount of disorder to the singular structure events Amplification of modulation by defects of integer numbers Establishing log-Poisson process : ln(ε) obeys Poisson distribution

Scale invariance: a feature of turbulence The multifractal formalism for turbulent flows - to describe the anomalous scaling properties of turbulence at large Reynolds numbers. Scale invariance of the Navier-Stokes equation: ∂tu + u · u = − p/ +[j. B]/c+ u u - velocity field, equation is invariant with respect to the scale : transformation - For viscosity ν = 0 any α. Parisi and Frisch proposed each fluctuation h at scale r is weighted with a probability distribution Ph(r) ~ r 3−D(h). Multi-scaling (multifractality)

Klimov, S. Romanov, E. Amata, J. Blecki, J. Buechner, J. Juchniewicz, J. Rustenbach, P. Triska, L. J. C. Woolliscroft, S. Savin, Yu. Afanas'yev, U. de Angelis, U. Auster, G. Bellucci, A. Best, F. Farnik, V. Formisano, P. Gough, R. Grard, V. Grushin, G. Haerendel, V. Ivchenko, V. Korepanov, H. Lehmann, B. Nikutowski, M. Nozdrachev, S. Orsini, M. Parrot, A. Petrukovich, J. L. Rauch, K. Sauer, A. Skalsky, J. Slominski, J. G. Trotignon, J. Vojta, R. Wronowski, ASPI Experiment: Measurements of Fields and Waves Onboard the INTERBALL-1 Spacecraft, Ann. Geophys. , v. 15, p. 514 -527, (1997). Savin S. P. , Zelenyi, L. M. , Amata, E. et al. , Dynanic Interaction of Plasma Flow with Hot Boundary Layer of Geomagnetic Trap, JETP Letters, 79, 452 -456, (2004)

T- 2 diagram: multifractal multiplicative cascade concentrated in closed domain Integral time T – dimensional parameter. Is it an additional scale in the process and symmetry?

Power spectra S(f)= n(f) 2 LCMS Edge, SOL Density , T-10 SOL q Bandwidth of drift-wave instabilities ~1 -1000 k. Hz q No monochromatic modes q No clear evidence of 1/f (Kolmogorov type) spectra over the whole frequency range In SOL typical d~-1. 5: -3, S(f)~fd

Space plasmas

T- 2 scales: feature of multifractal multiplicative cascade PDF of increments l. X=X(t+l)-X(t) structure function of increments has nonlinear scaling T-10 SOL M(q, l)= l. X q ~l (q)=q. H- 2 q 2 multifractality parameter PDF, l=300 PDF, l=1 2=0. 03 -0. 05 T 50 -200 s for fusion devices T 60 -80 sec for space plasma Coarse (mixing) time scale of T in the process: scale of coherent structures

Evidence of multifractality (multi-scaling) PDF of increments l. X(t)=X(t+l)-X(t), depends on scale l=1 -128 mc Shuffled data become Brownian with Gaussian increments

Функция распределения T-10, flux Ø Strong events happen more frequently than random ØStatistics varies strongly in space ØResembles power law Cauchy function T-10, density

Фурье спектры S(f)= n(f) 2 LCMS Edge, SOL Density , T-10 SOL q Bandwidth of drift-wave instabilities ~1 -1000 k. Hz q. No monochromatic modes q No clear evidence of 1/f (Kolmogorov type) spectra over the whole frequency range In SOL typical d~-1. 5: -3, S(f)~fd