- Email: [email protected]
The interpretation of measurements of radio-wave interaction
Research notes
If pl be the reflection coefficient at a frequency ji, and pz that at j2, then the collisional frequency v is given by ji log, Pl -A l%e Pe v = 2c area ABP,‘P,’ as shown in Fig. 1 when c is the velocity of light in vacuum, and P’s represent the group paths. The reflection coefficients were determined with a manually operated recorder in the Ionosphere Laboratory of the Institute of Radio Physics and Electronics, Calcutta University, and by using the method as given by CHATTERJEE(1952). The average diurnal variation curve of the collisional frequency is shown in Fig. 2. It is observed that the value of v is of the order of 103/sec, and becomes maximum (about 5 x 103/sec) near about noon, and minimum (about 102/sec) near about midnight. The diurnal variation curve for v was also plotted against cos x. But it was not linear. This shows another deviation of the F-region from the Chapman law. Actually, the rat,e of rise of v was found to increase with cos x, and this may be explained in terms of the rapid rise of temperature in the F-region with the approach of noon. MRINMAYEEGHOSH P&m
Women’s College, Pohu,
India REFERENCES
APPLETON, E. V.
CHATTERJEE, B.
1935 1952
INc&ure 135,618 Indian J. Phya. 26, 585
The interpretation of measurements of radio-wave interaction (Received 18 -4,ugusl1955)
THE theory of the interaction of radio waves in the ionosphere (BAILEYand MARTTN. 1!04. 1937, 1938) is based upon an equation for the time-dependence of the mean agitational energy Q of electrons moving among molecules of the air under the in%uence of the field of the disturbing radio wave. If w(t) is the power delivered to an electron by the radio wave, and R the rate at which electrons with energy Q lose energy in collisions with the molecules, then the basic equation is dQ/dt + R = w(t). (1) The quantity R, in a given gas, is a fun&ion of the agitational energies Q and Q0 of the electrons and gas molecules, such that R is evanescent as Q approaches QO. In the oriltinal formulation of the theory it’ was supposed that R = Gv(Q -
Q,),
(2)
where Y is-the collisional frequency of the electrons and 6’ a parameter whose value it. was hoped could be found from laboratory measurements of electronic motion in air. Measurements of radio-wave interaction, when interpreted in terms of this formulation of the theol,!-.
Research notes
led to values of the quantity Gv at the seat of the cross-modulation in the ionosphere: consequently it was considered that v could be found if G were known. When, however, the manner in which the quantity R is measured is considered, as well as the theory of its origin, it becomes evident that the introduction of the collisional frequency at this early stage is artificial, and that the physical quantity that is immediately concerned is the number of molecules in unit volume n, rather than v the collisionalfrequency of the electrons. It is suggested therefore that equation (2) should be replaced by R=
(3)
Bn(Q --f&J,
where B is a function of Q and Q. that is effectively constant when (Q/Q0 - 1) < 1. Thus the atmospheric parameter that it can be hoped to find directly from measurements of radio-wave interaction is not t,he collisional frequency v, but the molecular concentration n. In laboratory experiments, when electrons in a steady state of motion drift et speed W through a gas at pressure p under the action of an electric field 2, the power w = ZeW supplied to an electron is equal to the rate of loss of energy R in collisions. It follows that, if p is expressed in millimetres of mercury and Z in volts per centimetre, x 10” x 3.35 x 10’6 -&8 x 10-10
-- --
R/n = 2.09 Y lOmR/n = (Z/p)W.
Since both W and Q/Q0 are functions of Z/p, the lat,ter parameter may be eliminated and the experimental dependence of R/n on Q/Q0 determined in principle. In order to relate the experimental dependence of R upon Q/Q0 to the theory of radio-wave interaction, an approximate theoretical investigation was made of the loss of energy by electrons in those collisions that produce changes in the rotational energies of the molecules of diatomic gases. The following dependence of R upon Q and Q. was deduced, and was found to describe the experimental results corresponding to the.smaller values of Q/a: R/n =
aQ1'2[exp (-B/Q) - exp(-8/Qo)l,
c.g.s. units.
(4)
where a and B are constants. In oxygen at T = 288°K. when Q/Q0 < 7 the experimental results* are closely represented by this formula with a = 3-04 x IO-‘6 and p/Q0 = 14.4. In nitrogen, the measurements corresponding to small values of Q/Q0 are not sufficiently ext,ensive for accurate values of a and /3/Q, to be assigned, although it is evident that p/Q0 $ 3. In air, the quantity R is R = 0~2R,, + 0*8RNz, and it proves to be the case that when Q/Q0 > 7 t,he term 0*2Roz is predominant: but as Q + Q. the contribution of the oxygen to R in air is negligible. Thus when Q -+ Qo, Rair -+ 0.8Rnitrogen. Also, when (Q - Qo)/Qo < 1, equation (4) assumes the form: R/n + x/%exp
(-P/QoVQolQ-1~2(Q -~Qo).
(5)
A comparison of this formula and the extrapolated experimental results in nitrogen at T = 2W’K leads to the following special. but at present approximate, form of equation (5) applicable at any temperat,ure T:
(R/n)
[exp [---3( 1 -- T/28X)}] Q--‘12(Q --- Q,J.
119
Research
notes
If it be supposed that the temperature in the ionosphere at about 85 km above the ground is ZOO*K,and that in radio-wave interaction (Q - Q~)~Q~< 1, then (.Rfn)air= 0.8(Rf&it~o~en zzz8.5 \/ lo-l2 (Q -
Qo) = B (& -
Qg).
In observation of radio-wave interaction at oblique incidence (e.g., RATCLIFFEand SXKAW, 1948; HUXLEY, 1952), it was found that Bn (formerly CV) ranged from lo3 to 2.5 x 1P. The corresponding range of n is therefore 1.2 x 1O1”to 3 x I 014 cm-3. The corresponding range of heights is 83 to 89 km. These heights are consistent with the vadues determined from t$hephase of the cross-modulation. The collisional frequency v can be derived from n through the relationship v = nAtf, where d is the mean coflisional cross-section and 0 the mean speed of agitation of t,he electrons, provided the dependence of A upon 0 is known. It is found (C~o~o~, HUXLEY, and SUTTON,1953) that in air ~~he~~~~~ < 9, A = 2.48 x JWa31?. Since d = 4.33 Y J013Q1’2,it follows that Y = 4.9 x lO*nQ. The values of Y that, correspond to n = 1.2 Y lOI* and 3 Y 101@ when i” = 200°K are v = 24 x JO5 and 6.1 x J05. In order to determine the value of B more precisely, further laboratory values of R in nitrogen at small values of Q/Q0 are needed. These matters will be discussed in greater detail in anot’her paper. L. G. R. HUXLEY.
REFERENCES BAILEY, V. A.
HAILEY,~. A., and MARTYN,D.
F.
C’ROMX’TON, R. w., HUXLEY, L. G. H., and &‘ITON, D. .J.
1937 1938 1934 1935 1953
HusLEY,L.G.H.
1952
RATCLIFFE, J. A.. and SHAW,I, ;I.
1948
On the observation
PM. Mzg. a3, 929; &8, 426 Nature 135, 218; Phil. Ma+ 18, 369. Nature, 135, 585. Proc. Roy. Sot. A218, 507. NWVO Cimen&3 Supplement, ser. IX. f’m~. R
of ionospheric
vol.
IS,
self-inbction
A~~-E~en~~~l
p~~~tione are de8eribed that must be taken in e~primentai st~ud~s of ionouyherlc eelf-interaction to avoid misleading results caused by interference between various rays and hv the hand-widt,h of the mceiver, THERE is at present interest in, and some controversy ahout, the phenomenon of selfinteract.ion. The author has recently published (HIBBERD, 1955) a quantitative theory of the efiecfin the absence of a magnetic field, which should serve as a guide to experiment. The presence of the magnetic field complicates the sitnation, aud makes a qu&it,ative
If pl be the reflection coefficient at a frequency ji, and pz that at j2, then the collisional frequency v is given by ji log, Pl -A l%e Pe v = 2c area ABP,‘P,’ as shown in Fig. 1 when c is the velocity of light in vacuum, and P’s represent the group paths. The reflection coefficients were determined with a manually operated recorder in the Ionosphere Laboratory of the Institute of Radio Physics and Electronics, Calcutta University, and by using the method as given by CHATTERJEE(1952). The average diurnal variation curve of the collisional frequency is shown in Fig. 2. It is observed that the value of v is of the order of 103/sec, and becomes maximum (about 5 x 103/sec) near about noon, and minimum (about 102/sec) near about midnight. The diurnal variation curve for v was also plotted against cos x. But it was not linear. This shows another deviation of the F-region from the Chapman law. Actually, the rat,e of rise of v was found to increase with cos x, and this may be explained in terms of the rapid rise of temperature in the F-region with the approach of noon. MRINMAYEEGHOSH P&m
Women’s College, Pohu,
India REFERENCES
APPLETON, E. V.
CHATTERJEE, B.
1935 1952
INc&ure 135,618 Indian J. Phya. 26, 585
The interpretation of measurements of radio-wave interaction (Received 18 -4,ugusl1955)
THE theory of the interaction of radio waves in the ionosphere (BAILEYand MARTTN. 1!04. 1937, 1938) is based upon an equation for the time-dependence of the mean agitational energy Q of electrons moving among molecules of the air under the in%uence of the field of the disturbing radio wave. If w(t) is the power delivered to an electron by the radio wave, and R the rate at which electrons with energy Q lose energy in collisions with the molecules, then the basic equation is dQ/dt + R = w(t). (1) The quantity R, in a given gas, is a fun&ion of the agitational energies Q and Q0 of the electrons and gas molecules, such that R is evanescent as Q approaches QO. In the oriltinal formulation of the theory it’ was supposed that R = Gv(Q -
Q,),
(2)
where Y is-the collisional frequency of the electrons and 6’ a parameter whose value it. was hoped could be found from laboratory measurements of electronic motion in air. Measurements of radio-wave interaction, when interpreted in terms of this formulation of the theol,!-.
Research notes
led to values of the quantity Gv at the seat of the cross-modulation in the ionosphere: consequently it was considered that v could be found if G were known. When, however, the manner in which the quantity R is measured is considered, as well as the theory of its origin, it becomes evident that the introduction of the collisional frequency at this early stage is artificial, and that the physical quantity that is immediately concerned is the number of molecules in unit volume n, rather than v the collisionalfrequency of the electrons. It is suggested therefore that equation (2) should be replaced by R=
(3)
Bn(Q --f&J,
where B is a function of Q and Q. that is effectively constant when (Q/Q0 - 1) < 1. Thus the atmospheric parameter that it can be hoped to find directly from measurements of radio-wave interaction is not t,he collisional frequency v, but the molecular concentration n. In laboratory experiments, when electrons in a steady state of motion drift et speed W through a gas at pressure p under the action of an electric field 2, the power w = ZeW supplied to an electron is equal to the rate of loss of energy R in collisions. It follows that, if p is expressed in millimetres of mercury and Z in volts per centimetre, x 10” x 3.35 x 10’6 -&8 x 10-10
-- --
R/n = 2.09 Y lOmR/n = (Z/p)W.
Since both W and Q/Q0 are functions of Z/p, the lat,ter parameter may be eliminated and the experimental dependence of R/n on Q/Q0 determined in principle. In order to relate the experimental dependence of R upon Q/Q0 to the theory of radio-wave interaction, an approximate theoretical investigation was made of the loss of energy by electrons in those collisions that produce changes in the rotational energies of the molecules of diatomic gases. The following dependence of R upon Q and Q. was deduced, and was found to describe the experimental results corresponding to the.smaller values of Q/a: R/n =
aQ1'2[exp (-B/Q) - exp(-8/Qo)l,
c.g.s. units.
(4)
where a and B are constants. In oxygen at T = 288°K. when Q/Q0 < 7 the experimental results* are closely represented by this formula with a = 3-04 x IO-‘6 and p/Q0 = 14.4. In nitrogen, the measurements corresponding to small values of Q/Q0 are not sufficiently ext,ensive for accurate values of a and /3/Q, to be assigned, although it is evident that p/Q0 $ 3. In air, the quantity R is R = 0~2R,, + 0*8RNz, and it proves to be the case that when Q/Q0 > 7 t,he term 0*2Roz is predominant: but as Q + Q. the contribution of the oxygen to R in air is negligible. Thus when Q -+ Qo, Rair -+ 0.8Rnitrogen. Also, when (Q - Qo)/Qo < 1, equation (4) assumes the form: R/n + x/%exp
(-P/QoVQolQ-1~2(Q -~Qo).
(5)
A comparison of this formula and the extrapolated experimental results in nitrogen at T = 2W’K leads to the following special. but at present approximate, form of equation (5) applicable at any temperat,ure T:
(R/n)
[exp [---3( 1 -- T/28X)}] Q--‘12(Q --- Q,J.
119
Research
notes
If it be supposed that the temperature in the ionosphere at about 85 km above the ground is ZOO*K,and that in radio-wave interaction (Q - Q~)~Q~< 1, then (.Rfn)air= 0.8(Rf&it~o~en zzz8.5 \/ lo-l2 (Q -
Qo) = B (& -
Qg).
In observation of radio-wave interaction at oblique incidence (e.g., RATCLIFFEand SXKAW, 1948; HUXLEY, 1952), it was found that Bn (formerly CV) ranged from lo3 to 2.5 x 1P. The corresponding range of n is therefore 1.2 x 1O1”to 3 x I 014 cm-3. The corresponding range of heights is 83 to 89 km. These heights are consistent with the vadues determined from t$hephase of the cross-modulation. The collisional frequency v can be derived from n through the relationship v = nAtf, where d is the mean coflisional cross-section and 0 the mean speed of agitation of t,he electrons, provided the dependence of A upon 0 is known. It is found (C~o~o~, HUXLEY, and SUTTON,1953) that in air ~~he~~~~~ < 9, A = 2.48 x JWa31?. Since d = 4.33 Y J013Q1’2,it follows that Y = 4.9 x lO*nQ. The values of Y that, correspond to n = 1.2 Y lOI* and 3 Y 101@ when i” = 200°K are v = 24 x JO5 and 6.1 x J05. In order to determine the value of B more precisely, further laboratory values of R in nitrogen at small values of Q/Q0 are needed. These matters will be discussed in greater detail in anot’her paper. L. G. R. HUXLEY.
REFERENCES BAILEY, V. A.
HAILEY,~. A., and MARTYN,D.
F.
C’ROMX’TON, R. w., HUXLEY, L. G. H., and &‘ITON, D. .J.
1937 1938 1934 1935 1953
HusLEY,L.G.H.
1952
RATCLIFFE, J. A.. and SHAW,I, ;I.
1948
On the observation
PM. Mzg. a3, 929; &8, 426 Nature 135, 218; Phil. Ma+ 18, 369. Nature, 135, 585. Proc. Roy. Sot. A218, 507. NWVO Cimen&3 Supplement, ser. IX. f’m~. R
of ionospheric
vol.
IS,
self-inbction
A~~-E~en~~~l
p~~~tione are de8eribed that must be taken in e~primentai st~ud~s of ionouyherlc eelf-interaction to avoid misleading results caused by interference between various rays and hv the hand-widt,h of the mceiver, THERE is at present interest in, and some controversy ahout, the phenomenon of selfinteract.ion. The author has recently published (HIBBERD, 1955) a quantitative theory of the efiecfin the absence of a magnetic field, which should serve as a guide to experiment. The presence of the magnetic field complicates the sitnation, aud makes a qu&it,ative