Magnetospheric MHD Resonances and ULF Pulsations - Ultra and Extremely Low Frequency Electromagnetic Fields - page 265

To study the shape of resonance components, E x and ıB y , in a little more detail
we use the representation of Q x 1 in the form

1
Q x D

exp .i'/
n .x n / 2

C ı n o 1=2 ;

(6.144)

where the argument ' of complex number is determined via

ı n
x n

tan ' D : (6.145)

2

It is clear from Eq. ( 6.144 ) that near the resonant point the dependence j E x j

and LJ LJ ıB y LJ LJ

2

on x has a form of Lorentz's curve outlined in Fig. 6.3 . The normalized
component LJ LJ ıB y LJ LJ

2

versus normalized variable x= n is sketched in this figure with
solid line 1. The Lorentz's curve has a maximum at x D n and the parameter j ı n j
is the characteristic half-width of this maximum. The argument/phase ' of E x and
ıB y changes by when crossing the maximum. A schematic plot of the component
ıB x is shown in Fig. 6.3 with dashed line 2.
In conclusion it should be noted that if V A .x/ is not a monotonic function there
may be more turning and resonance points.

References

Alperovich LS, Fedorov EN (2007) Hydromagnetic waves in the magnetosphere and the iono-
sphere. Springer, Berlin, 426 pp
Anderson RV (1982) The dependence of space charge spectra on Aitken nucleus concentrations.
J Geophys Res 87:1216-1218
Anisimov SV, Mareev EA, Bakastov SS (1999) On the generation and evolution of aeroelectric
structures in the surface layer. J Geophys Res D 104:14359-14367
Anisimov SV, Mareev EA, Shikhova NM, Dmitriev EM (2002) Universal spectra of electric field
pulsations in the atmosphere. Geophys Res Lett 29(24):2217. doi:10.1029/2002GL015765
Annexstad JO, Wilson ChR (1968) Characteristics of Pg micropulsations at conjugate points.
J Geophys Res 73:1805-1818
Atkinson G, Watanabe T (1966) Surface waves on the magnetospheric boundary as a possible
origin of long period micropulsations. Earth Planet Sci Lett 1:89-91
Baransky LN, Borovkov YuE, Gokhberg MB, Krylov SM, Troitskaya VA (1985) High resolution
method of direct measurement of the magnetic field lines eigenfrequencies. Planet Space Sci
33:1369-1374
Baransky LN, Belokris SP, Borovkov YuE, Green CA (1990) Two simple methods for the deter-
mination of the resonance frequencies of magnetic field lines. Planet Space Sci 38:1573-1576
Baumjohann W, Glassmeier KN (1984) The transient response mechanism and Pi2 pulsations at
substorm onset: review and outlook. Planet Space Sci 32:1361-1370
Burov VA, Lapshin VB, Syroezhkin AV (2013) Space weather and air traffic. World of measure-
ments (Mir Izmereniy), No. 2. pp 11-16 (in Russian)
Chalmers JA (1967) Atmospheric electricity, 2nd edn. Pergamon, New York