12
WHISTLER-TRIGGERED VLF EMISSIONS RECORDED AT JAMMU DURING DAY TIME
Ravindra Pratap Patel*1 and Krishna Kumar Singh2*12

Department of Physics, M. M. H. (P. G.) College, Ghaziabad (U.P.) India
Dept. of Physics, Indian Institute of Technology, Banaras Hindu University, Varanasi, India
Corresponding Author: rppatel12@yahoo.co.in; rppatel123@rediffmail.com

How to cite this paper:
Patel, Ravindra Pratap andSingh, Krishna Kumar (2022)
Whistler-triggered
VLF
emissions recorded at Jammu
during day time, Journal ofGlobal Resources, Vol. 08 (01)

DOI:10.46587/JGR.2022.v08i01.012

Received: 01 Nov. 2021
Reviewed: 15 Nov. 2021
Revised: 30 Nov, 2021
Final Accepted: 11 Dec. 2021

Abstract: Whistler-triggered VLF emissions recorded at low
latitude station Jammu (Geomagnetic latitude = 220 26/ N; L =1.17) during day time period on 19th February 1999 at 14:35
hrs. IST. The recorded data have been analyzed. Based onwhistler-triggered VLF emissions spectrum, the VLF waves
propagate along the path with L – values lying between L = 4.4
and 4.38. During the observation period, magnetic activity wasvery high. Mostly these types of emissions recorded at midlatitudes. These whistler-triggered emission waves propagate
along the geomagnetic field lines either in a ducted mode or ina pro-longitudinal mode. Relative amplitude of whistlers waves
is almost equal to relative amplitude of triggered emissions.
The proposed generation mechanism explains through thedynamic spectra of the whistler-triggered emissions.
Key words: Whistlers, Triggered Emissions, Wave-Particle
Interaction, Resonance Conditions.

Journal of Global Resources, January 2022, Volume 08 (01) Ravindra P. Patel and Krishna Kumar Singh Page | 103

Introduction
Whistlers are electromagnetic waves whose energy originates from natural lighting discharges
and propagate through the magnetosphere, whereas VLF emissions are electromagnetic waves(a)generated by wave-particle
interactions occurring in the Earth’s magnetosphere (Helliwell, 1965).
The wave particle interactions occurring in the magnetosphere generates a variety of emissions
in VLF range. These emissions, both continuous or unstructured and discrete or structured innatural are very fascinating, challenging and interesting natural phenomena. These emissions
are classified into hiss, discrete chorus, hook and inverted hook, periodic and quasi-periodic andtriggered emissions (Helliwell, 1965, Nunn and Smith, 1996). Some signal receives from VLF
transmitters (Helliwell, 1965; Bell et al., 1982) and some types of chorus emissions arise from theupper frequency of hiss (Helliwell, 1969, Reeve and Rycroft, 1971, Koons, 1981 Hattori et at.,1989, Singh et al., 2000a). Many observations support the idea that strong VLF emissions may
be triggered even by very weak signals. The second order cyclotron resonance along an
inhomogeneous dipolar magnetic field was discussed by (Helliwell, 1967, Nunn, 1974, Karpman
et al., 1974) and has become very useful in theories of triggered emissions. In this paper, wepresent a details analysis of whistler-triggered emissions observed at a low latitude Indian station
Jammu during day time. These events propagate along the higher L-values lying between 1.9
and 4.4 as compared to be observation station Jammu (L = 1.17). Thus, the waves are a part of
mid latitude whistlers that may have propagated through the Earth ionosphere wave guide
towards the equator. The proposed generation mechanism is a nonlinear cyclotron interaction
between whistler triggered emissions and counter streaming energetic electrons. Someparameters have been calculated numerically such as parallel resonance energy, trapping time,
Bunching time, oscillation period for the trapped electrons.
Experimental observations and Data Analysis
At low latitude ground station Jammu, the wideband VLF signals are recorded by T-type antenna,
suitably amplified by pre and main amplifiers and recorded using a tape recorder. The recorded
waves were analyzed by Advance VLF Data Analysis System (AVDAS) and sonograms. Some
dynamic spectra of whistler triggered emissions are presented. In Figure 1c shows that two eventsof whistler triggered emissions recorded on February 19, 1999 at 14:35 hrs. (IST) in which discretechorus risers are triggered from bottom side of the whistler spectrums. During the observation
period Kp – index was 6- to 3- and Dst index is -106, which is shown in figure 1a,b. The firstobserved whistler wave frequency varies between 5.3 kHz to 8.4 kHz and second event is 4.3
kHz to 8.5 kHz whereas the frequency of triggered chorus emission varies between 5.1 kHz and7.9 kHz in the first event and 4.5 kHz and 7.1 kHz in the second event. The relative intensity ofwhistler wave and triggered chorus emissions are given in triggered emission is almost same.
The df/dt value of triggered emission is 1.38 kHz/sec and 1.41 kHz/sec for first and second event
respectively. The dispersion of whistler is 88.9 S1/2 and 88.6 s1/2, corresponding path of
propagation is L = 4.4 and 4.38 for the first and second waves respectively.
Table 01: Relative intensity of whistler and Triggered emission of figure 01c.
Whistler wave
Frequency (kHz)
8.4
7.6
6.8
6.1
5.3

Relative
intensity (dB)
58
59
60
61
61

Frequency (kHz)
7.9
7.6
6.8
6.1
5.1

Triggered emissions
Relative
intensity (dB)
58
59
60
61
61

Journal of Global Resources, January 2022, Volume 08 (01) Ravindra P. Patel and Krishna Kumar Singh Page | 104

(a)

(b)

(c)

Figure 01: (a) Variation of KP - index. (b) Variation of Dst – index. (c) Dynamic spectrum of thewhistler-triggered emissions recorded at Jammu on 19th February 1999 at 14:35 hrs. (IST)
Generation Mechanism
The non-linear self-consistent resonant interaction of energetic electrons with narrow band VLF
waves in the Earth’s magnetosphere has been used to explain many of the qualitative physicalfeatures underlying triggered emissions (Helliwell, 1967; Karpman et al., 1974; Yoshida et al.,
1983; Molvig et al., 1988; Omura et al., 1991; Nunn et al., 1997; Trakhtengerts and Rycroft, 2000).
A large number of workers have been made to solve the problem using different numerical modelsuch as sheet current model (Helliwell and Inan, 1982; Carlson et al., 1990), non-linear resonantcurrent model (Nunn, 1984), electromagnetic full particle model (Cuperman and Lyons, 1974;
Omura and Matsumoto, 1987), fluid-particle (hybrid) model (Vomvoridis and Denavit, 1980;
Vomvoridis et al., 1982) and Vlasov hybrid model (Nunn, 1990; Nunn and Smith, 1996). On thebasis of non-linear cyclotron resonant interaction between whistler mode waves and counter
streaming energetic electrons, the cyclotron resonance condition is written as⍵ - ⍵H /𝛾 = k v||(1)
Journal of Global Resources, January 2022, Volume 08 (01) Ravindra P. Patel and Krishna Kumar Singh Page | 105

Where ⍵ and k are the wave frequency and wave vector of the whistler waves, k = |k|, ⍵H is theelectron gyro-frequency, v|| is the field aligned component of the electron velocity, 𝛾 = (1 – v2 /c2)-1/2 is the relativistic factor, v and c is the interacting particle velocity and light velocity in freespace. For ducted whistler propagation K||B0, B0 being the vector geomagnetic field. In an
inhomogeneous magnetic field, ⍵H, v|| and k are functions of the coordinate z along the magnetic
field B0. The electrons with different v|| interact with the same wave (⍵, k) at different points along
the geomagnetic field lines.
According to non-linear theory, the field equation for slowly varying in magnetic field canbe written as (Omura et al., 1991; Trakhtengerts and Rycroft, 2000)(∂/∂t + vg ∂/∂z) B⍵ = (µ0/2) vg JR(2)where B⍵ is the complex amplitude of the magnetic wave field, vg is the group velocity and JR isthe current due to the resonant electrons. The dispersion relation for the whistler mode waves
propagating along the geomagnetic field line is given as
k = [ (⍵P ⍵1/2/c (⍵H ─ ⍵)1/2 ](3)where ⍵P is the electron plasma frequency. Combing equation (1) and (3), the resonant electronenergy is written as
ER = mVR2 /2(4)where m is the mass of electron. The resonance velocity VR = V││ written as
VR = [c cosα (ωH ─ ω)1/2 [ωH {( ωH + ω)( ωH ─ ω)2 + ω2P ω cos2α}1/2
─ ωP ω3/2 cosα]]/[ ω2H (ωH ─ ω) + ω2P ω cos2α]5)Where α is the pitch angle of the electron. In our numerical computation for relativistic
parallel resonance energy, we have used normalized electron density verses distance along thefield line from the equator according to the collision-less model. We have taken equatorial electron
density 550 and 65 electrons cm-3 for two path of propagation L= 3 and 4.5 respectively and thecorresponding plasma frequency is ~ 211, 72 kHz and electron gyro-frequency is ~ 32 and 9 kHz.
Calculate the value of parallel velocity is V││ ~ 2.48 × 108 m/s and perpendicular velocity is V┴ ~0.64 × 108 m/s, which is parallel velocity is greater than the perpendicular velocity of resonant
electron. Using equation (4), we calculate the value of relativistic parallel resonance energy for L= 3 and 4.5 for pitch angle (α = 300) and different wave frequency of electrons. We found that theER ~ 6.61 × 103 keV to 0.003 keV For L = 3, wave frequency varies between 0.1 to 30 kHz, andfor L = 4.5, frequency varies between 0.1 to 8 kHz, ER decreases from 764 keV to 0.028 keV. The
resonant energy decreases with increasing wave frequency. Thus, it is clearly seen that in the
inner magnetosphere high energy particles are actually participating in the triggering process. As
pitch angle (α) increases, resonant electron energy increases but the overall pitch angle
dependence is non-linear. For low latitude ground station Varanasi, the interaction region
corresponding to inner magnetosphere for L =2, 3 and 4, ER varies between Mev to keV havepresented by (Patel, 2002; Singh et al., 2003).
If the rates of change of electron gyrofrequency and of the wave frequency balance eachother, then the electron will remain in resonance for a longer duration and the phase angle
remains constant. This means that the full derivative of equation (1) along the particle path iszero, which is the idea of second order resonance, first formulated by (Helliwell, 1967). This was
suggested to be the necessary condition for the most effective wave-particle interaction in theinhomogeneous magnetic field. The resonant electrons are then phase bunched by the (eV┴ ×Bω) force acting along the field line. Solving equation of motion of an electron traveling in an
inhomogeneous medium, in the presence of a whistler wave, it can be shown that the wave
trapped electrons oscillate with a period (Dysthe, 1971; Inan et al., 1978; Yoshida et al., 1983)
Tr = {(2πmVP)/(eV┴ f Bω)}1/2(6)Journal of Global Resources, January 2022, Volume 08 (01) Ravindra P. Patel and Krishna Kumar Singh Page | 106

where m is the mass of electron, e is the charge of electron, f is the wave frequency, Bω is thewave magnetic field, VP = ω/k is the phase velocity, V┴ is the velocity of the electron perpendicular
to the field. The trapped electron oscillates with a frequency Ωtr = (keV┴ Bω/m)1/2. Yoshida et al.
(1983) have concluded that electrons whose absolute initial phase (φ) is less than 900, will bebunched at φ = 00 after a period of Tr/4 is called as bunching time (TB). We have used someparameters for computing bunching time, wave frequency f = 1 kHz, φ = 00, Bω = 1mγ, α = 150,bunching time TB ~ 17 ms for L = 2. The same for L = 4.5 is 54 ms. The initial geomagnetic latitude
increases with decreasing bunching time. Also wave magnetic field increases, bunching time isdecreases. As wave frequency increases as in the presence of dense plasma, bunching timedecreases.
Conclusions
In this paper, we present detailed spectral analysis of whistler triggered emissions observed at
the low latitude ground Jammu during daytime period. Based on observations and computations
reported following some point emerge.
1. Whistler-triggered emission waves are recorded at low latitude ground station Jammu forthe first time during daytime period.
2. The KP – index and Dst – index was very high during the observation period.
3. These events may actually be mid-latitude emissions, because our analysis of whistler
waves propagated along geomagnetic field line is higher L-values lying between 4.4 and
4.38.
4. They are propagated along the geomagnetic field lines (4.38 ≤ L ≤ 4.4) and after exitingfrom the ionosphere and excite the Earth-ionosphere wave guide and propagate towardsthe equator along with whistlers.
5. The relative amplitude of whistlers and triggered emissions are almost same.
6. The relativistic parallel resonance energy of electrons decreases with increasing
frequency but energy increases with decreasing L-value. The reported resonance electronenergy lies in the kev range.
7. Bunching time decreases with increasing of both geomagnetic latitude and wave magnetic
field. Wave frequency increases as in the presence of dense plasma, bunching timedecreases.
Acknowledgements: R. P. Patel is thankful to Professor Lalmani for providing whistler-triggered
VLF emissions data.
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