SOVIET PHYSICS JETP VOLUME 24, NUMBER 2 FEBRUARY, 1967 SPLITTING OF IONIC LINES OWING TO REVOLUTION OF THE IONS IN A MAGNETIC FIELD M. I. D'YAKONOV A. F. Ioffe Physico-technical Institute, Academy of Sciences, U.S.S.R. Submitted to JETP editor March 12, 1966 J. Exptl. Theoret. Phys. (U.S.S.R.) 51, 612-616 (August, 1966) It is shown that if the cyclotron frequency Q of the revolutions of an ion in a magnetic field ex- ceeds the natural width 'Y of a spectral line, then in the radiation directed transverse to the magnetic field the Doppler contour of each Zeeman component is split into a number of peaks. The distance between adjacent peaks is Q, and the width of each peak is determined by the natural line width 'Y. IT is well known that for a gas at not too high pressure the width of an atomic or ionic line is due to the Doppler effect, and as a rule consider- ably exceeds the natural line width 'Y. In the present paper it is shown that if a plasma is placed in a sufficiently strong magnetic field, then in the radiation in a direction transverse to the field the spectral lines of the ions are decidedly altered in shape. Namely, when the condition Q 'Y is satisfied, where Q is the Larmor frequency of the ion, the Doppler contour of an ionic line is split into a series of peaks with widths equal to the natural line width 'Y and separated from each other by the amount Q. Accordingly, when observed transverse to the magnetic field, the contour of such a line takes the form shown in the figure. This sort of splitting occurs for each of the Zee- man components of the line (the distance between Zeeman components is larger than the splitting considered here by a factor where M is the mass of the ion and m that of the electron). The explanation of this effect is extremely sim- ple. In a sufficiently strong magnetic field an ion makes several revolutions in a Larmor orbit dur- ing the time of emission of radiation. For Q > 'Y the revolving radiator emits in the plane of revo- lution a discrete spectrum of frequencies w 0 + nQ, where w 0 is the characteristic frequency of the stationary radiator, Q is the angular frequency of revolution, and n = 0, ± 1, ± 2, .... Since the fre- quency of revolution Q of the ion does not depend on its velocity and is determined only by the mag- netic field, in the direction perpendicular to the magnetic field all of the ions emit the same spec- trum of frequencies. The only thing dependent on the velocity of the ion and the phase of its revolu- tion is the distribution of the radiated energy over t f{(W) I Splitting of an individual Zeeman component of an ionic line observed transverse to the magnetic field [Eq. (8)]; rry/fl = 1, ku/0 = 10. The dashed curve is the Doppler contour as ob- served for y >> 0. this spectrum; this will of course be different for different ions. Averaging over the ions leads to the spectrum shown in the figure. These qualitative arguments are confirmed by the following simple calculation. Let the magnetic field H be directed along the z axis, and let the spontaneous emission from the ions be observed in the direction of the x axis. We denote the transi- tion frequency for a chosen Zeeman component of an ionic line by w 0 , and the natural line width by 'Y· In a semiclassical treatment the field E(t) pro- duced by one ion at the point of observation x 1 is of the form E(t) = EA(t), A (t) = exp[i(iwo- V / 2) (t- to) - ik(x 1- x(t)) + i¢]. (1) Here t 0 is the time at which the atom became ex- cited, k = w 0 /c, x(t) is the coordinate of the ion along the x axis at the time t, and 1/J is the initial phase. The amplitude E of the electric field is 408