Short wavelength drift waves in a magnetic quadrupole

Abstract

A linear thcor) is dcielopcd for drift iiitvcs Bith frequencies betiiecn the electron and ion bouncc frequencics in a collisionless plasma confined to a magnetic quadrupole. A n integro-direreniial cifcntaluc equation U hich allot+s for large ion-Larmor-radius cffccts. temperature gradients. and radial \nri;ition of the eigenrunction is dcriied from the linearized Viasot equation. The fundamental drift mode obscrtcd in the L'MIST stcadj-state quadrupole has one full ttaielength around a closed magnctic field line nith the electrostatic w a t e potential antisJmmciric about the maximum field points. BJ numsrical mitition or the cigcnialue equation. the theoretical dispersion curie for this mode IS extended t o short t i a i c l e n g t h ~ and the \ariation of the corrtsponding potential along a field line 1s determined. I . I S T R O D L ' C T I O SESPERISlEsTAL studies of electrostatic wives in a plasma confined to a magnetic quadrupole are current13 being carried out at the Lnii,ersity of Jlanchester Institute of Science and Technology (UMIST). Drift ivaves x i t h one full u.a\elength around a closed magnetic field line ha\,e been observed to occur spontaneously. C.ARTER et d. (1951 ) ha1.e made a theoretical and experimental study of these drift Lvaves in the UMIST quadrupole. Their theoretical and experimental dispersion curves are in good agreement throughout the entire axial \vave number range from k, 2 0 . 6 cmi to k , 2 1.6 cm-'. The general shape of the theoretical curws shoiving ~a v e amplitude variation along a field iine is also ~vc.11 reproduced b! the experimental results in this k , range. This mode is belicxd to be excited b! . a dissipati\,e trappcdclcctron mechanism \vhich \vas in\,cstigated recently by NI'ILLETT. i ~i tri. ( 19S6)..Although the obsei\'ed spectrum of spontaneous drift \\'a\ es in the ChI!ST

Damping and destabilization of drift waves by electron-neutral collisions

“…It is interesting to compare these results with the growth rate due to electron-neutral detrapping collisions only. The equation for i' due to detrapping collisions (WILLETT et al, 1986) differs from equation ( 16) in that the rl(Tl(@)) term in the integrand is absent and V is replaced by the electronneutral detrapping collision frequency which in the present case is 0.1 6V. Also, in the present analysis the ion-Larmor-radius parameter b has been retained to all orders.…”

“…Recently the operator L(w) was derived (WILLETT, et al, 1986) in the following form which allows for large ion-Larmor-radius effects and temperature gradients: 3) is restricted to wave frequencies between the electron and ion bounce frequencies.…”

“…To derive this operator, the collision term was added to the Vlasov equation for the electron distribution function f e . The derivation will be omitted herein since it is a straightforward generalization of one presented elsewhere (WILLETT et al, 1986). The result is where Me is the electron mass, and the electron-neutral collision frequency 1' = v(u) is a function of the electron speed E .…”

“…Destabilization of this mode is believed to be due to a dissipative trapped-particle mechanism involving electron-neutral collisions. A formula for the growth rate due to detrapping collisions only which is restricted to a mode antisymmetric about the maximum field point was derived in the small ion-Larmor-radius approximation by WILLETT et al (1986). Self-interaction of this fundamental drift mode produces an excitation at twice its frequency which may drive the next harmonic drift mode with two full wavelengths around a closed field line and symmetry about the maximum and minimum field points.…”

Use of generalized parameters for the description of dispersion characteristics of channel waveguides

“…The former, which occurs spontaneously for axial wave numbers k between 60radm-' and 170radm-', has been identified by Carter et al [l] as a dissipative trapped electron drift mode, driven by detrapping electron-neutral collisions (Willett et al [3] and Aktas et al [4]). The eigenvalue equation for this mode was first solved by Carter et al [l] for small axial wave numbers k and later by Willett et al [5] for large k, including finite ion Larmor radius effects to all orders. For long wavelengths, k c 60radm-', this mode is stabilized by ion Landau damping, Uddholm et al [SI, but the processes responsible for its stabilization at short wavelengths, k > 170 rad m-', still remain unidentified.…”