Biskamp, D.

Elsässer , K.

Pfirsch, D.

English

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Second European conference on contro lled fusion and plasma physics 467 ] f the particle remains inside a thin tube of radius ro centred about r where ro is of the order of the characteristic d istance of the field variation, then the particle is said to be confined and r is called the • I d" ' P asma ra IUS. By taki ng into account the expansion parameters Go (Larmor radius/plasma radius) and e (plasma radius/mean radius of curvature) toget her, an adiabatic type theory ean be developed, which takes fini te Larmor radius effects into account in the basic periodic solut ion of the problem . The expansion pammelcr is in fact : Larmor radius EGO = mean radius of curvature ' In the first-o rder approximation eGo, the principal terms which appear only in the second-order approximation of the cl.:tssic.:tl adiabatic theo ry (parameter Go) arc found . The equations arc no longer valid if the particle departs too far from the tube, but this case is not of in terest since these part icles arc no longer confined. The 'guiding cent rc' equations obtained are thus valid in the thin tube approximation, even if the Larmor radius is of the same order as the plasma radius. The cITect of singll larities in the magnetic field at in tegral values o f the rotat ional transform on the magnetic axis, can be s tudied, as well as the reRection of particles with Iow Vu due to a mirror effect of the toroidal field . Certain cases are completely .integrable to this order, and provide a s imple illustra-tion or the phenomena. Non-linear resonance effects at high power in a cylindrical plasma * A. M. MESSIAEN and P. E . VANDENPLAS Laboratoire de Physique des Plasmas, Ecole Royale Mil itaire. Bruxelles 4, Belgium A PLASMA column exhibits a main resonance and series of secondary resonances whcn a low power electromagnetic wave (with El. axis and flU axis) is di rected on it a nd when the density is varied by altcring the discharge current. The co rresponding phenomena are now investigated at high power (E-fie lds up to 10' Vm- l). A luminosity curve gives an independent measurement of plasma dens ity as a function of diSCharge current. When E > 103 Ym- 1 , strong non-linear effects appear : deformation of the different resonance peaks and hysteresis, the corresponding luminosity cu rve exh ibits kin ks indicating greater perturbation of the average plasma density over a wider resonance domain. As the power increases, the kinks become plateaux indicating preferential absorption of energy at resonance and a tendency or the plasma to remain in a resonant state through h.f. ionization. With high incident energy. the high amount of energy absorbed at resonance is sufficient to sustain the plasma in a resonant state in the absence of a d.c. discharge cu rrent . The absorbed h.f. energy remains practically constant as a function of increasing incoming energy when the plasma is self-sustained in one of its eigenmodes ; the corresponding density also remains practically constant as indicated by the luminosity. When the incoming h.f. energy is decreased below a certain minimum, there is a jump to the next resonance characterized by a lower density. '" Presented by P. E . VANDENPLAS. Paper published in Pllys. Le/l. 2SA, 339 (1967). Kinetic equations for microscopic turbulence' D. PFIRSCH, K. ELSAS.<;ER ann n. RISK AMP Max-PIanck-Institut fUr Physik und Astrophysik, Munich Federal Republic of Germany Two types of kinetic equations for the homogeneous microscopic ttlfbuience of a onc-dimensional plasma are compared with each other. These a re the usual quasilinca r approach and a theory based on the Hamilton-Jacobi formalism. Both theories should yicld the same results as long as particle trapping can be neglected. We est imate that this becomes important for times of the order of '" Presented by D. PFIRSCH. I m2 v,,(.6.v .. )3 T= - . 2.1.:1. W l1 e't' 468 B. LEHNERT here 11" is a typical phase velocity in a reference system with vanishin rr group velocity and nu is the range of phase vclo~i[ics for the unstable modes . F,or times sn~all c~mparcd to T the two theories agree, whereas for tUlles of the order of T the Hanlllton-JacobJ approach deviates from the quasi-linear theory in a way which can be interpreted as a relaxation effect. Instability and anomalous diffusion of a weakly ionized magnetized radio-frequency plasma * J. POLMAN Philips Research Laboratories , N . V. PhiJips' Glocilampcnfabrickcn Eindhovcn, Netherlands THE infl uence of a magnetic field on the transverse din'usion of a weakly ionized radio-frequency hydrogen plasma has been investigated by measuring the density decay of the plasma along the mag~ netic fie ld, directed parallel to the discharge tube (inner diameter 5 cm, Icngth 200 cm). Thc plasma is created at onc cnd of this tube. The :lxial decay length is inversely proporlional to the square root of the transverse diO'usion coenlcient. The range of prcssures used was 0,02-0,07 torr. At low values of the magnetic field (~50-70 G) the transverse diO'usion coefficient behaves c1assic;:llly, while at higher fields the transverse din'lIsion becomes anomalolls, its coefficient being independent of gas pressure and magnetic field . At the critical field Dcr , whcre anomalous diffusion begins, the plasma bccomcs unstable, showing oscillations with frequencies of about 100 kc/s and higher harmonics of this [rc~ qucncy. At highcr fields the oscillations disappear in strong random fluctuations. Dct is proportional to the square root of the gas pressure. An explanation of the above phenomena, based on the theory of the ion acoustic instability of a weakly ionized inhomogeneous plasma by Timofeev, can be given, from which the values of the critical field and the oscillation spectrum can be derived. The results o f the diffusion coefficient measurements can be explained by introducing the turbulent mixing length concept in the theory of a plasma, subjected to ion acoustic instability. '" Presented by the author. Paper published in Plasma Phys. 9, 471 (1967); also available as a Thesis, University of Groningen, Natuurkundig Lab. der R.U., Groningen, Netherlands . Fusion efficiency for revolving fields' M. L. POOL, J. W. SNYDER, P. E . WEtLER and P. POLISHUK Ohio State University, Columbus, U.S.A . IN A d.c. magnetic bottle a hydrogen plasma has been created by the magnctic and elcctric fields induced by two sets of four coils. One phase of a two~phase 4'O~MHz oscillator energizes two coils of each set. and the other phasc energizes the other two coils. The strength of the magnetic bottle fie ld is that required for ion-cyclotron resonance. Thomson scattering from a ru by laser beam indicates a particle density of 2 x 1013 cm-3 to date . The salient ability of the coil ensemble to (a) walk ions to the centre of the plasma and (b) to give them an energy corresponding to that in an orbit of a radius which is 5 per cent less than the radius of the vacuum chamber but no more energy, is corroborated. An extension of this coil ensemble is proposed. Two such ensembles as above would be placed in the same magnet ic bottle field and made to operate upon two parallel and c011linuously connected vacuum chambers. Onc coil ensemble would be energized at a cyclotron frequency of A and the other ensemble. properly phased. at a frequency of E, where AID = 3/2. A mixture of deuterium and tritium would be admitted . The two cyclotronic beams would react in the connected regions of the chambers. Calculations indicate that for the two ion beams, each at the terminal energy of 44·5 keY and at regional densities of about 1016 cm-3 , an energy yicld could be obtained which is equal to the energy inherent in the beams. '" Presented by M . L. POOL. Work sponsored by a grant from the Air Force Office of Scientific Research, Washington D .C . and in part by the Air Force F light Dynamics Laboratory. 

Kinetic Equations for Microscopic Turbulence

http://hdl.handle.net/21.11116/0000-0008-BD41-A

Kinetic Equations for Microscopic Turbulence

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