Electron velocity distribution and the interpretation of cross-modulation experiments

Journalof Atmoephericand TerrestrialPhysics,1969,Vol. 51, pp. 863-854. PergamonPreaa. Printedin NorthernIreland

SHORT PAPER

Electron velocity distribution and the interpretation of cross-modulation experiments N. N. PURKAIT and B. R. NAU Centre of Advanced Study in Radio Physics and Electronics, University of Calcutta 4 December

(Received

1968)

Abstract-The change in ionospheric conductivity produced by a disturbing field depends on the energy loss factor B. The three possibilities that B is independent of electron energy, E, or varies like E-l or E-1’2, are discussed.

earlier paper (NAG and PURKAIT, 1968) the authors discussed the low-field conductivity of the D-region of the ionosphere in the presence of a high-field disturbing signal assuming the electron-neutral particle collisions to be elastic. It was concluded that substantial errors may occur in theinterpretationof cross-modulation experiments if the electron velocity distribution function is assumed to be Maxwellian. In the present note results for non-elastic collisions are given. These results have been obtained by using the procedure outlined in the earlier paper. The energy loss factor, G has been assumed to vary with the electron energy, E according to either of the following two relations: IN AN

(i) G = G,,E-f (ii) G = GJV;

;

(PHELPS, (HUXLEY,

1963; 1959;

BELL, FROST

1966)

and PHELPS, 1962).

The ratio of the change in conductivity appropriate to the wanted signal, obtained from the non-Maxwellian distribution function (AC,,), to that obtained from the equivalent Maxwellian distribution function, (ACT,), varies with the disturbing field as shown in figure 1. The disturbing field has been normalised by a critical field defined as Fc = :

(3G,,,kTm,)’

where ezz is the electron mass, k is the Boltzmann constant, T is the temperature of the neutral particles, G,,, and rm are respectively the values of G and collision frequency Y for electrons of energy kT. The data used in the calculations are the same as used in the earlier paper. For the sake of comparison, the results for elastic collisions are also included. We find from Fig. 1 that the ratio (AaNlll/AoM) has its highest value for the case of elastic collisions, but is decreased in magnitude for non-elastic collisions. At fields 853

N. N. PURKAIT and B. R. NAG

864

Fig. 1. Ratio of the change in conductivity of the wanted signal obtained from the non-Maxwellian distribution function, A~NM, and that obtained from the equivalent Maxwellian distribution function AUM, for different normalised disturbing fields (F/F,).

of the order of the critical field the difference is less than40 per cent for G proportional to E-t and less than 20 per cent for G proportional to E-1, as compared to a difference of about 100 per cent for elastic collisions. Thus, the error that may arise from the assumption of Maxwellian distribution in the interpretation of cross-modulation experiment will be substantially reduced for non-elastic collisions. Acknowledgeme&--The

authors are indebted to Professor J. N. Bhar for his constant guidance.

REFERENCES FROST L. S.and PHELPS A.V. HUXLEY L.G.H. NAU B. R. and PURKAIT N. N.

1962 1969 1968

Phy.9. Rev. 127, 1621. J. Atmosph. Tern. Phys. 16, 46. J. Atmosph. Terr. Phys. 30, 1465.

Reference is also made to the following unpublished work BELL C. D.

1966

PHELPSA. V.

1963

Ionosph. Res. Lab. Scient. Rep. No. 262, The Pennsylvania State University. Presented at the Conference on non-linear processes in the ionosphere Boulder, Colo. Dec. 14-19. NBS Tech Note No. 211, 49.