TY - JOUR
T1 - Transport equation describing fractional Ĺvy motion of suprathermal ions in TORPEX
AU - Bovet, A.
AU - Gamarino, M.
AU - Furno, I.
AU - Ricci, P.
AU - Fasoli, A.
AU - Gustafson, K.
AU - Newman, D. E.
AU - Sánchez, R.
PY - 2014/10/1
Y1 - 2014/10/1
N2 - Suprathermal ions, created by fusion reactions or by additional heating, will play an important role in burning plasmas such as the ones in ITER or DEMO. Basic plasma experiments, with easy access for diagnostics and well-controlled plasma scenarios, are particularly suitable to investigate the transport of suprathermal ions in plasma waves and turbulence. Experimental measurements and numerical simulations have revealed that the transport of fast ions in the presence of electrostatic turbulence in the basic plasma toroidal experiment TORPEX is generally non-classical. Namely, the mean-squared radial displacement of the ions does not scale linearly with time, but r2(t)∼tγ, with γ≠1 generally, γ>1 corresponding to superdiffusion and γ<1 to subdiffusion. A generalization of the classical model of diffusion, the so-called fractional Ĺvy motion, which encompasses power-law (Ĺvy) statistics for the displacements and correlated temporal increments, leads to non-classical dynamics such as that observed in the experiments. On a macroscopic scale, this results in fractional differential operators, which are used to model non-Gaussian, non-local anomalous transport in a growing number of applied fields, including plasma physics. In this paper, we show that asymmetric fractional Ĺvy motion can be described by a diffusion equation using space-fractional differential operator with skewness. Numerical simulations of tracers in TORPEX turbulence are performed. The time evolution of the radial particle position distribution is shown to be described by solutions of the fractional diffusion equation corresponding to asymmetric fractional Ĺvy motion in sub- and superdiffusive cases.
AB - Suprathermal ions, created by fusion reactions or by additional heating, will play an important role in burning plasmas such as the ones in ITER or DEMO. Basic plasma experiments, with easy access for diagnostics and well-controlled plasma scenarios, are particularly suitable to investigate the transport of suprathermal ions in plasma waves and turbulence. Experimental measurements and numerical simulations have revealed that the transport of fast ions in the presence of electrostatic turbulence in the basic plasma toroidal experiment TORPEX is generally non-classical. Namely, the mean-squared radial displacement of the ions does not scale linearly with time, but r2(t)∼tγ, with γ≠1 generally, γ>1 corresponding to superdiffusion and γ<1 to subdiffusion. A generalization of the classical model of diffusion, the so-called fractional Ĺvy motion, which encompasses power-law (Ĺvy) statistics for the displacements and correlated temporal increments, leads to non-classical dynamics such as that observed in the experiments. On a macroscopic scale, this results in fractional differential operators, which are used to model non-Gaussian, non-local anomalous transport in a growing number of applied fields, including plasma physics. In this paper, we show that asymmetric fractional Ĺvy motion can be described by a diffusion equation using space-fractional differential operator with skewness. Numerical simulations of tracers in TORPEX turbulence are performed. The time evolution of the radial particle position distribution is shown to be described by solutions of the fractional diffusion equation corresponding to asymmetric fractional Ĺvy motion in sub- and superdiffusive cases.
KW - fast ions
KW - fractional diffusion
KW - Levy motion
KW - nondiffusive transport
KW - plasma physics
KW - stable distributions
KW - suprathermal ions
UR - http://www.scopus.com/inward/record.url?scp=84907942156&partnerID=8YFLogxK
U2 - 10.1088/0029-5515/54/10/104009
DO - 10.1088/0029-5515/54/10/104009
M3 - Article
AN - SCOPUS:84907942156
SN - 0029-5515
VL - 54
JO - Nuclear Fusion
JF - Nuclear Fusion
IS - 10
M1 - 104009
ER -