Conventional and nonconventional global Alfvén eigenmodes in stellarators

Abstract

Conditions of the existence of the Global Alfvén Eigenmodes (GAE) and Nonconventional Global Alfvén Eigenmodes (NGAE) predicted for stellarators by Ya. I. Kolesnichenko et al. [Phys. Rev. Lett. 94, 165004 (2005)] have been obtained. It is found that they depend on the nature of the rotational transform and that conditions for NGAE can be most easily satisfied in currentless stellarators. It is shown that the plasma compressibility may play an important role for the modes with the frequency about or less than that of the Toroidicity-induced Alfvén Eigenmodes (TAE). It is found that features of the Alfvén continuum in the vicinity of the k = 0 radius (k is the longitudinal wave number) can be very different, depending on a parameter which we refer to as "the sound parameter". Specific calculations modeling low-

Drift-sound and drift-Alfvén eigenmodes in toroidal plasmas

“…LF instabilities occur in all types of toroidal plasma systems. In particular, Reversed Shear Alfvén Eigenmodes (RSAE) or Alfvén Cascades (AC) were observed in JET and extensively studied theoretically [4,5]; Non-conventional Global Alfvén Eigenmodes (NGAE) were predicted to exist in stellarators and seem to be observed in Wendelstein 7-AS (W7-AS) [3,6]; Beta-induced Alfvén Acoustic Eigenmodes (BAAE) were observed in the NSTX spherical torus [7], the Sound Cascades (SC) were observed in ASDEX-Upgrade [8]. Despite efforts of many theorists, a number of features of experimentally observed LF instabilities remain a mystery.…”

“…A condition of the existence of discrete eigenmodes (not necessary well localized) is U 1 (r) < 0 in some region, which provides the presence of two "turning points". Discrete eigenmodes exist even when U 1 (r) < 0 in the whole plasma cross section provided that Ψ(a) = 0, with a the plasma radius [3].…”

“…-Recently, instabilities with frequencies below that of the Toroidicity-induced Alfvén Eigenmodes (TAE) attracted considerable attention in fusion research. These Low Frequency (LF) instabilities may strongly deteriorate the confinement of fast ions [1]; they are not necessarily harmful, in which case they can be used for plasma diagnostics [2,3]. LF instabilities occur in all types of toroidal plasma systems.…”

“…Equation (6) is written with taking into account that the harmonics with high µ, ν weakly contribute to ω G (see ref. [3]); in addition, the harmonics of B 0 with µ > 1 are neglected (therefore, ω G is somewhat underestimated).…”

“…and ω * e = mcT e n e /(e e Bn e r), with p i the ion pressure, prime denotes the radial derivative, ν ι is the fraction of the rotational transform produced by the plasma current (ν ι = 1 in tokamaks, ν ι = 0 in currentless stellarators), δ 0 1 characterizes the plasma shape [3],…”