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Discussion on theories of movement of ionospheric irregularities
inNorthern Ireland Journal ofAtmospheric andTerrestrial Physics, 1069,Vol.31,pp.193to196. Pergamon Press.Printed
SHORT PAPER
Discussion on theories of movement of ionospheric irregularities SUSUMU KATO* and SADAMI MATSUSHITA High Altitude
Observatory,
(Received 12 April
Boulder, Colorado 1968)
Al&act-This short note seems to answer the question as to whether there are any serious discrepancies in the velocity of irregularities between Kato’s theory and Tsedilina’s one. It is found that both theories reach the same result for linear weak irregularities and the difference is only superficial. But only K&o’s theory is applicable to strong irregularities.
SINCE 1963 Kato (KATO, 1963,
has published
1964,
1965u, b;
a series of papers about
ionization
KATO and MATSUSHITA, 1968).
irregularities
TSEDILINA (1965)
also has recently discussed the movement of irregularities. The result of both theories seems to have confused some readers because of apparent differences. This needs to be examined as observations of the movement of presumably similar irregularities are now in progress (e.g. WRIGHT and FEDOR, 1967) and a critical review of our theory will be attempted by the present authors based on those observations. Denote, hereafter, Kato’s Theory, Theory I and Tsedilina’s, Theory II. Firstly, both Theories I and II assume perturbations (irregularities) only in charged particles, but none in neutral particles. Note, however, that these theories are different in that Theory I is applicable to dense as well as weak irregularities while Theory II is applicable only to weak irregularities. Secondly, both theories assume a quasi-stationary state, in which the inertia of charged particles is entirely neglected and the displacement current is also neglected as can be understood by div J = 0 in Theory I (J = electric current density) and div (NV,) = div (NV,) in Theory II (see equation 11; N = number density of electrons and ions, V,,i = velocities of electrons and ions). These basic assumptions common in both Theories I and II should lead us to the same results. Note that both theories neglect diffusion effects, but only Theory I considers the induction i3B/& where B is the magnetic field and t is time (equation (2.15), KATO, 1963); this induction field proves insignificant under normal conditions, however. The equation of motion in Theory II is erroneous in that it contains N only in the first term on the left side, however, this error disappears in further steps. * On leave from Kyoto 13
University,
Kyoto,
Japan.
193
STJSUMO KATOand SADAXIMATSUSHITA
194
The difference between the two theories, therefore, should be very minor or else they might be applied to different situations. A superficial difference is that in Theory I the electric current J and conductivities G@,~,~ (oO = parallel conductivity, cl = Pedersen conductivity, cr2= Hall conductivity) are often used while in Theory II E only is used. Note, in this connection that the collision between ions and electrons seems to be considered only in Theory II, but this can be included at will in CT~,~,~ also in Theory I. Analysis of results in Theory II consists of two cases; in case (A) there is no a’pplied electric field and in case (B) there exists only an applied electric field. This means that in case (A) only the dynamo field (U, x B,) where U, is the neutral wind velocity, drives the ambient stationary current Jo which is normal to B,. Theory I shows that under this condition the phase velocity of linear weak irregularities relative to U, is (equation (ll), KATO, 1964)
(1) where w = frequency, k = wave vector, m, and Mi = mass of electrons and ions, Y&i = electron and ion collision frequencies with neutral particles. The above relation is valid unless the angle between k and B,, is 90” within a few degrees of accuracy. Such irregularities may move as fast as the lzeutral ionization drift (MARTYN,1953) which is not much different from the ion velocity Vi because (e.g. equation (lo), KATO, 196&f 1 Jo x B, + ; B,J, vi = N( I m,Vp_ + Mivi) 8 where the second term in the bracket is, above 90 km height, much smaller than the first term giving the neutral ionization drift (C?,,= electron gyrofrequency). Of course, if U, is parallel to B,,, J, = 0 and hence w/k= 0; irregularities move exactly with U,. And if k is very nearly normal to B,, Theory I gives 0.J -=
k
k
JcN(m,v,+ Mivi)
Jo x B. - 2 B,Jol
I
m f . V,
where Joi is Jo normal to B. and V, electron’s velocity. These results in Theory I are the same as those in Theory II. In case (B) Jo is not always normal to BO. But the electric field component parallel to B0 is almost always much smaller than that normal to B0 above 90 km height because of G,,> orr2. Then, the result of Theory I is the same as that in case (A). This indicates that linear weak irregularities, not exactly field-aligned, move approximately with the neutral ionization drift which further can be approximated to the ion veZ~~~~as illustra~ in Fig. 1 (KATO, 1964). In this diagram U,, depends on the eIectric current parallel to B,, and U, depends on the electric current normal to BO,whereit is given that
co/% =
0; .u
u = u,,+ UL.
Discussion on theories of movement of ionospheric irregularities
195
The maximum of U,, occurs when k is very nearly normal to B, for cr2/g1 > 1. Note that the ordinate of the curves in Fig. 1 is shown by (U,,/V,) divided by (E,,,/E,,) where E,,,, and J&L are the applied electric field E0 parallel and normal to B0 respectively. This factor (E,,,/E,,) is extremely small, say 10-2. The value of (U,,/U,) can be obtained from ( U,,/V,)/(EO,,/EOl) by multiplying by the factor(E,,,/ _7&). Then, U w UL is valid in almost all cases, which shows that the movement of irregularities depends only on the electric field or current normal to B,,. Theory II raises other possibilities which are, however, impractical being based on E,,,, M E ,,l. Then, we also have no significant difference in case (B) between both theories. 2or
Fig. 1. (UII/U,_) vs. 6, the angle between k and BO. a and b correspond to the case where aJo, = 20 and uO/aI= 1,000 and the case where a,/q = l/2 and ~,,/a~= 10,000, respectively: E,,,~/EOl,the ratio of the applied electric field along B, and that normal to B,. This ratio usually is much smaller than unity, say 10e2, and hence UII/U, < 1.
The velocity U in Theory I corresponds to V, in Theory II. Unlike V,, U is always normal to B,. At first glance this difference may seem significant. However, the addition of any velocity normal to k produces no changes in the phase velocity. As the phase velocity is the only physically significant parameter, the apparent difference in U and V, becomes arbitrary. A serious question now arises as to whether the irregularities really observed are linear weak wave irregularities. Irregularities such as meteor trails or artificial ion clouds (B,+-clouds) are dense in ionization, which is against the assumption in Theory II. It should be pointed out, however, that Theory I shows the asymptotic Strong non-linear irregularities behavior of irregularity with increasing ionization. tend to be free from the applied electric force as the polarization field set-up tends to cancel the applied field. They then tend to move with the neutral gas, which is known to be usually the case for meteor trails (KENT and WRIGHT, 1968). There are apparently also irregularities of another kind such as those which produce
196
SUSUMUKATO and SADAMI MATSUSHITA
fading patterns of radio wave signals reflected from the ionosphere (D-l method). These irregularities may be represented by weak linear waves, which move approximately with the ions, as is discussed above. This means that their horizontal velocity relative to the neutral air motion should amount to 10 m set-l or less at 100 km height. It is still unclear, however, whether or not the observations (e.g. WRIGHT and FEDOR, 1967) can be precisely explained by Theories I and II which give the same answer on the movement of these linear weak irregularities. In still another application these theories are valid (KATO, 1964) in understanding the movement of field-aligned irregularities moving as fast as electrons (equation 2’) in equatorial sporadic-E (BOWLES et al., 1963) and other irregularities perhaps rarely seen anywhere else. Both Theories I and II may be vulnerable for assuming no perturbation in neutral particles. Those irregularities which are separated from the source producing them satisfy this assumption, while those near the source should share somehow the velocity of the source which may be gravity waves or turbulence. In the (upper) P-region the charged particles react back to neutral particles fairly quickly. Then, the interaction between charged and neutral particles become important. These concepts are outside the scope of both Theories I and II, but an extension of the theory in this direction is desirable. Also, it is vitally important to measure the ionospheric movement by various methods all at once and compare their results in detail. REFERENCES BOWLES K. L., BALSLEY B. B. and COHENR. ‘KATOS. KATO S. KATO S. KATO S. KATO S. and MATSUSHITAS. KENT G. S. and WRIUHT R. W. H. MARTYN D. F. TSEDILINA Y. Y. WRIGHT J. W. and FEDOR L. S.
1963
J. Geophys. Res. 68, 2485.
1963 1964 1965a 19656 1968 1968 1953 1965 1967
Planet. Space hi. 11,823. Planet. Space Sci. 12, 1. Space Sci. Rev. 4, 223. J. Atmosph. TOW. Phys. 27, 373. J. Atmosph. Terr. Phys. 30, 857. J. Atmosph. Terr. Phys. 30, 657. Phil. Trans. R. Sot. A246, 306. Geomag.Aeron. 5, 525. Space Research VII p. 67, NorthHolland, Amsterdam.
SHORT PAPER
Discussion on theories of movement of ionospheric irregularities SUSUMU KATO* and SADAMI MATSUSHITA High Altitude
Observatory,
(Received 12 April
Boulder, Colorado 1968)
Al&act-This short note seems to answer the question as to whether there are any serious discrepancies in the velocity of irregularities between Kato’s theory and Tsedilina’s one. It is found that both theories reach the same result for linear weak irregularities and the difference is only superficial. But only K&o’s theory is applicable to strong irregularities.
SINCE 1963 Kato (KATO, 1963,
has published
1964,
1965u, b;
a series of papers about
ionization
KATO and MATSUSHITA, 1968).
irregularities
TSEDILINA (1965)
also has recently discussed the movement of irregularities. The result of both theories seems to have confused some readers because of apparent differences. This needs to be examined as observations of the movement of presumably similar irregularities are now in progress (e.g. WRIGHT and FEDOR, 1967) and a critical review of our theory will be attempted by the present authors based on those observations. Denote, hereafter, Kato’s Theory, Theory I and Tsedilina’s, Theory II. Firstly, both Theories I and II assume perturbations (irregularities) only in charged particles, but none in neutral particles. Note, however, that these theories are different in that Theory I is applicable to dense as well as weak irregularities while Theory II is applicable only to weak irregularities. Secondly, both theories assume a quasi-stationary state, in which the inertia of charged particles is entirely neglected and the displacement current is also neglected as can be understood by div J = 0 in Theory I (J = electric current density) and div (NV,) = div (NV,) in Theory II (see equation 11; N = number density of electrons and ions, V,,i = velocities of electrons and ions). These basic assumptions common in both Theories I and II should lead us to the same results. Note that both theories neglect diffusion effects, but only Theory I considers the induction i3B/& where B is the magnetic field and t is time (equation (2.15), KATO, 1963); this induction field proves insignificant under normal conditions, however. The equation of motion in Theory II is erroneous in that it contains N only in the first term on the left side, however, this error disappears in further steps. * On leave from Kyoto 13
University,
Kyoto,
Japan.
193
STJSUMO KATOand SADAXIMATSUSHITA
194
The difference between the two theories, therefore, should be very minor or else they might be applied to different situations. A superficial difference is that in Theory I the electric current J and conductivities G@,~,~ (oO = parallel conductivity, cl = Pedersen conductivity, cr2= Hall conductivity) are often used while in Theory II E only is used. Note, in this connection that the collision between ions and electrons seems to be considered only in Theory II, but this can be included at will in CT~,~,~ also in Theory I. Analysis of results in Theory II consists of two cases; in case (A) there is no a’pplied electric field and in case (B) there exists only an applied electric field. This means that in case (A) only the dynamo field (U, x B,) where U, is the neutral wind velocity, drives the ambient stationary current Jo which is normal to B,. Theory I shows that under this condition the phase velocity of linear weak irregularities relative to U, is (equation (ll), KATO, 1964)
(1) where w = frequency, k = wave vector, m, and Mi = mass of electrons and ions, Y&i = electron and ion collision frequencies with neutral particles. The above relation is valid unless the angle between k and B,, is 90” within a few degrees of accuracy. Such irregularities may move as fast as the lzeutral ionization drift (MARTYN,1953) which is not much different from the ion velocity Vi because (e.g. equation (lo), KATO, 196&f 1 Jo x B, + ; B,J, vi = N( I m,Vp_ + Mivi) 8 where the second term in the bracket is, above 90 km height, much smaller than the first term giving the neutral ionization drift (C?,,= electron gyrofrequency). Of course, if U, is parallel to B,,, J, = 0 and hence w/k= 0; irregularities move exactly with U,. And if k is very nearly normal to B,, Theory I gives 0.J -=
k
k
JcN(m,v,+ Mivi)
Jo x B. - 2 B,Jol
I
m f . V,
where Joi is Jo normal to B. and V, electron’s velocity. These results in Theory I are the same as those in Theory II. In case (B) Jo is not always normal to BO. But the electric field component parallel to B0 is almost always much smaller than that normal to B0 above 90 km height because of G,,> orr2. Then, the result of Theory I is the same as that in case (A). This indicates that linear weak irregularities, not exactly field-aligned, move approximately with the neutral ionization drift which further can be approximated to the ion veZ~~~~as illustra~ in Fig. 1 (KATO, 1964). In this diagram U,, depends on the eIectric current parallel to B,, and U, depends on the electric current normal to BO,whereit is given that
co/% =
0; .u
u = u,,+ UL.
Discussion on theories of movement of ionospheric irregularities
195
The maximum of U,, occurs when k is very nearly normal to B, for cr2/g1 > 1. Note that the ordinate of the curves in Fig. 1 is shown by (U,,/V,) divided by (E,,,/E,,) where E,,,, and J&L are the applied electric field E0 parallel and normal to B0 respectively. This factor (E,,,/E,,) is extremely small, say 10-2. The value of (U,,/U,) can be obtained from ( U,,/V,)/(EO,,/EOl) by multiplying by the factor(E,,,/ _7&). Then, U w UL is valid in almost all cases, which shows that the movement of irregularities depends only on the electric field or current normal to B,,. Theory II raises other possibilities which are, however, impractical being based on E,,,, M E ,,l. Then, we also have no significant difference in case (B) between both theories. 2or
Fig. 1. (UII/U,_) vs. 6, the angle between k and BO. a and b correspond to the case where aJo, = 20 and uO/aI= 1,000 and the case where a,/q = l/2 and ~,,/a~= 10,000, respectively: E,,,~/EOl,the ratio of the applied electric field along B, and that normal to B,. This ratio usually is much smaller than unity, say 10e2, and hence UII/U, < 1.
The velocity U in Theory I corresponds to V, in Theory II. Unlike V,, U is always normal to B,. At first glance this difference may seem significant. However, the addition of any velocity normal to k produces no changes in the phase velocity. As the phase velocity is the only physically significant parameter, the apparent difference in U and V, becomes arbitrary. A serious question now arises as to whether the irregularities really observed are linear weak wave irregularities. Irregularities such as meteor trails or artificial ion clouds (B,+-clouds) are dense in ionization, which is against the assumption in Theory II. It should be pointed out, however, that Theory I shows the asymptotic Strong non-linear irregularities behavior of irregularity with increasing ionization. tend to be free from the applied electric force as the polarization field set-up tends to cancel the applied field. They then tend to move with the neutral gas, which is known to be usually the case for meteor trails (KENT and WRIGHT, 1968). There are apparently also irregularities of another kind such as those which produce
196
SUSUMUKATO and SADAMI MATSUSHITA
fading patterns of radio wave signals reflected from the ionosphere (D-l method). These irregularities may be represented by weak linear waves, which move approximately with the ions, as is discussed above. This means that their horizontal velocity relative to the neutral air motion should amount to 10 m set-l or less at 100 km height. It is still unclear, however, whether or not the observations (e.g. WRIGHT and FEDOR, 1967) can be precisely explained by Theories I and II which give the same answer on the movement of these linear weak irregularities. In still another application these theories are valid (KATO, 1964) in understanding the movement of field-aligned irregularities moving as fast as electrons (equation 2’) in equatorial sporadic-E (BOWLES et al., 1963) and other irregularities perhaps rarely seen anywhere else. Both Theories I and II may be vulnerable for assuming no perturbation in neutral particles. Those irregularities which are separated from the source producing them satisfy this assumption, while those near the source should share somehow the velocity of the source which may be gravity waves or turbulence. In the (upper) P-region the charged particles react back to neutral particles fairly quickly. Then, the interaction between charged and neutral particles become important. These concepts are outside the scope of both Theories I and II, but an extension of the theory in this direction is desirable. Also, it is vitally important to measure the ionospheric movement by various methods all at once and compare their results in detail. REFERENCES BOWLES K. L., BALSLEY B. B. and COHENR. ‘KATOS. KATO S. KATO S. KATO S. KATO S. and MATSUSHITAS. KENT G. S. and WRIUHT R. W. H. MARTYN D. F. TSEDILINA Y. Y. WRIGHT J. W. and FEDOR L. S.
1963
J. Geophys. Res. 68, 2485.
1963 1964 1965a 19656 1968 1968 1953 1965 1967
Planet. Space hi. 11,823. Planet. Space Sci. 12, 1. Space Sci. Rev. 4, 223. J. Atmosph. TOW. Phys. 27, 373. J. Atmosph. Terr. Phys. 30, 857. J. Atmosph. Terr. Phys. 30, 657. Phil. Trans. R. Sot. A246, 306. Geomag.Aeron. 5, 525. Space Research VII p. 67, NorthHolland, Amsterdam.