The solution of the relativistic equation of motion of a charged particle in a homogeneous magnetic and a rotating electric field perpendicular to each other

Hakkenberg, Anneke; Weenink, M. P. H.

doi:10.1016/0031-8914(64)90044-8

Cited by 15 publications

(8 citation statements)

References 1 publication

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“…where 7= [1+(p/m 0 c) 2 ] 1 / 2 . Neglecting the relativistic phase detuning effect [24], we obtain mv. 'icr = 5.2 X 10' 1 6 n(m" 3 ) frr=W cr (eV)…”

Section: Wave Propagation and Absorption From Ray-tracing Calculationsmentioning

confidence: 99%

Toroidal plasma production by electron cyclotron heating in the WT-2 device

Cho¹,

Ogura²,

Andõ³

et al. 1986

Nucl. Fusion

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By injecting microwave power (120 kW, 35.6 GHz) into the WT-2 device, a toroidal plasma is produced by electron cyclotron heating near the upper-hybrid resonance. (1) The production mechanism is interpreted as the result of damping of electron Bernstein waves and described by a ray-tracing code. (2) The production mechanism of high-energy electrons in such a plasma is studied and interpreted as a competition between electron acceleration by the incident wave and deceleration by collisions. These electrons interact resonantly with the lower hybrid wave during the startup of an RF tokamak discharge. (3) The first experimental observation, in an ECR plasma, of the resulting macroinstability, consistent with a theory suggested by Peng et al., is reported. (4) This instability is suppressed by the lower-hybrid driven current, the required rotational transform being produced by this current.

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“…where 7= [1+(p/m 0 c) 2 ] 1 / 2 . Neglecting the relativistic phase detuning effect [24], we obtain mv. 'icr = 5.2 X 10' 1 6 n(m" 3 ) frr=W cr (eV)…”

Section: Wave Propagation and Absorption From Ray-tracing Calculationsmentioning

confidence: 99%

Toroidal plasma production by electron cyclotron heating in the WT-2 device

Cho¹,

Ogura²,

Andõ³

et al. 1986

Nucl. Fusion

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“…This is explained as follows: The maximum energy gain AW lmax due to ECH is limited by the detuning (out of phase) between the electron gyration and the wavefield, which is caused by the third term in Eq. (4); AW ±max is given by [13,37] AW lmax (eV) = elEl mwc 2/3 (8) Assuming E = 100 V-cnr 1 , AW lmax is estimated to be about 1 keV. The perpendicular heating of AW leads to an increase of 0:…”

Section: Production Mechanism Of Hot Electrons By Ech Due To the Doppmentioning

confidence: 99%

“…To become hot, the electrons must at first surpass the critical velocity v = v cr derived in Ref. [37] from…”

Section: Dependence Of the Plasma Parameters On Various Operating Conmentioning

confidence: 99%

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A Functional Connected With a Surface of Given Mean Curvature

Mosolov¹

1969

Math. USSR Sb.

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Microwave power, P ECH < 140 kW, has been injected at 28 GHz into the axisymmetric plug/barrier cell in the axisymmetrized tandem mirror GAMMA 10. As observed by soft X-ray measurements, the microwaves generate a hot (50-60 keV) electron population, radially peaked on the magnetic axis, which results in the formation of a thermal barrier. The production mechanism of these hot electrons is found to be second harmonic electron cyclotron heating (ECH), corrected for the effects of the relativistic mass variation and the Doppler shift. This mechanism also explains the first experimental observation of a saturation of the single-component hot electron temperature T eh as being caused by the finite width of the incident microwave lobe. The dependence of the plasma parameters on the filling gas pressure, the plasma density and the ECH power is studied. It is found that the heating process can be interpreted as a competition between electron acceleration by the incident wave, electron deceleration by collisions, and the mirror trapping efficiency of the source electrons for hot electrons. The axial profile of the soft X-rays is investigated in relation to the mechanism of the second harmonic ECH. The heating process is discussed in terms of the electron pitch angle and the magnetic field intensity.

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“…The energy absorption of electrons initially at rest has been calculated by Hakkenberg and Weenink [13]. The detection of the cyclotron resonance therefore required a phase locked operation of an oscillator at this frequency.…”

Section: The Electron Cyclotron Resonancementioning

confidence: 99%

A direct determination of the proton-electron mass ratio

GÄrtner

Klempt

1978

Z Physik A

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The cyclotron resonance of protons and electrons in a magnetic field of 5.7 Tesla produced by a superconducting solenoid has been measured. Protons and electrons were alternately confined in an electrostatic quadrupole trap. The quotient of the cyclotron frequencies provides a first direct determination of the proton-electron mass ratio. The result of MJMe= 1836.1502 (53) agrees with other more precise but indirect determinations of this quantity.

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The solution of the relativistic equation of motion of a charged particle in a homogeneous magnetic and a rotating electric field perpendicular to each other

Cited by 15 publications

References 1 publication

Toroidal plasma production by electron cyclotron heating in the WT-2 device

Toroidal plasma production by electron cyclotron heating in the WT-2 device

A Functional Connected With a Surface of Given Mean Curvature

A direct determination of the proton-electron mass ratio

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