by
Rezy Pradipta
in partial fulfillment of the requirements for the degree of
Bachelor of Science in Physics
June 2006
@ Rezy Pradipta, MMVI. All rights reserved.
MASSAC
OF
HUSETS INSTURE
TECHNOLOGv
JUL 0 7 2006
........ I
..................
I IRRA:Ic
May 12, 2006 ARCHNIVES
I
.-... .....................
Certified by ...................
Min-Chang Lee
by .................... -. .
.
..
Dvid- E. Pritchard

by
Submitted to the Department of Physics on May 12, 2006, in partial fulfillment of the requirements for the degree of
Bachelor of Science in Physics
A series of incoherent scatter radar (ISR) observation were conducted at the Arecibo
Observatory from December 27, 2005 until January 3, 2006. From plasma line measurements that were taken during this radar campaign, we found that plasma line enhancement was quite frequently seen in the ionospheric E-region. We hypothesized that the E-region plasma line enhancement over Arecibo was caused by precipitated electrons from the radiation belts. The precipitated electrons will enhance the population of suprathermal electrons in the E-region. Subsequently, suprathermal electrons will cause excitation of Langmuir waves that could be detected by incoherent scatter radar as plasma lines. In this thesis, we are going to examine and discuss the observed features of E-region plasma line enhancement over Arecibo to test this hypothesis. In addition, a theoretical discussion on Langmuir waves is also presented in a chapter of this thesis. Finally, we also introduce the Spread F Index (SFI) as a convenient bookkeeping method to summarize spread F condition over a certain period of time.
Thesis Supervisor: Min-Chang Lee
Title: Head, Ionospheric Plasma Research Group
Plasma Science and Fusion Center
Thesis Supervisor: Richard Temkin
Title: Associate Director, Plasma Science and Fusion Center
Department of Physics
3

4

I would like to thank Prof. Min-Chang Lee as my undergraduate research advisor who had supervised my UROP and Thesis work at MIT Plasma Science and Fusion
Center (PSFC). All research experience that I gained since freshman year until the completion of this senior thesis is certainly one of the most valuable asset for me.
I am grateful that Prof. Lee had given me the opportunity to explore the field of ionospheric/space plasma physics through a large number of tutorial lectures, reading recommendations, and research projects. Finally, I would like to thank Prof. Lee for reviewing this senior thesis, correcting any conceptual mistakes, and providing suggestions for improvements.
I would also like to thank all my fellow students at MIT PSFC's ionospheric/space plasma research group for a truly amazing teamwork in experiments, data analysis, as well as theoretical discussions. They have shown their strong dedications while working in the Arecibo radar control room, adjusting front optics of our all-sky imager on the roof, and analyzing hundreds of gigabytes of plasma line spectra. I feel very lucky to have them as team members.
5

6

1 Introduction
1.1 Background and Context . . . . . . . . . . . . . . . .
.
. . . . .
.
1.2 The Hypothesis ..............................
9
9
10
2 Langmuir Waves
2.1 Propagation of Langmuir Waves in Magnetized Plasma: Fluid Equation Approach . . . . . . . . . . . . . . . .
.
. . . . . . ......
2.2 Landau Damping of Langmuir Waves ..................
15
16
21
3 Data and Discussion 27
3.1 Arecibo Radar Campaign During December 2005 /January 2006 . . .
27
3.2 E-Region Plasma Line Enhancement ..................
3.3 Data Highlights ..............................
28
30
3.3.1 December 28 - December 29, 2005 ...............
3.3.2 January 1 - January 2, 2006 ...................
3.3.3 January 2 - January 3, 2006 ...................
30
32
34
4 Conclusion 37
A Spread F Index
A.1 Ionosonde, Ionogram, and Spread F ...................
A.2 Spread F Index ...................
39
39
. . . . . . . . . . .
41
7

8

Introduction
During our December 2004 radar campaign at the Arecibo Observatory, several cases of plasma line enhancement in the ionospheric E-region were observed-in addition to a relatively rare case of F-region plasma line enhancement. We therefore conducted another radar campaign for several nights at the Arecibo Observatory starting on
December 27, 2005 and ending on January 3, 2006. The main goal of this incoherent scatter radar observation was to investigate E-region and F-region plasma line enhancement more closely. Therefore, plasma line measurements were taken much more extensively during the December 2005 /January 2006 radar campaign than during the previous (December 2004) radar campaign.
In this thesis, we focus on discussing the observation of plasma line enhancement in the ionospheric E-region conducted in December 2005/ January 2006. It was found that plasma. line enhancement in the ionospheric E-region occurred quite frequently during our observation hours. Based on this data, we therefore have a good opportunity to explore the features of E-region plasma line enhancement over Arecibo.
We are going to discuss some physics of Langmuir waves in the second chapter of this thesis, because plasma line signals are Langmuir waves detected by the incoherent scatter radar. This will include the dispersion relation of Langmuir waves in magnetized plasmas and the collisionless damping of Langmuir waves. Meanwhile, in
9

the third chapter of this thesis, we are going to present the result of our observation of E-region plasma line enhancement over arecibo. This will include a discussion of some general features of typical E-region plasma line enhancement over Arecibo and the highlights of a few special trends observed on some of the nights.
We suspect that E-region plasma line enhancement over Arecibo was caused by electrons that precipitate from the radiation belts into the lower ionosphere. The precipitated electrons from the radiation belts typically have initial kinetic energy of a few hundreds of keV. As these electrons traverse through the Earth's atmosphere, they will cause ionizations of neutral particles in the atmosphere. Thus, at the altitude where these precipitated electrons are finally stopped (in ionospheric E-region), a layer of anomalous ionizations will be created. In addition, after ionizing atmospheric neutrals, these precipitated electrons will have residual energy in the order of a few eV, which is significantly larger than the thermal energy of -0.1 eV. Thus, the precipitated electrons will enhance the population of suprathermal electrons in the ionospheric E-region, thereby exciting a spectrum of Langmuir waves at around
100 km altitude. While the density of the ionization layer is rather low, the generated Langmuir waves are expected to be able to produce backscatter signals that are intense enough to be detected as plasma lines by the incoherent scatter radar. This scenario is illustrated in Figure 1-1.
An additional factor that we have to take into account is a powerful radio transmitter, called NAU, which is located in a nearby town of Aguada, PR. NAU transmits very-low-frequency (VLF) radio signals at the frequency of 40.75 kHz with a transmitted power of approximately 100 kW. Some of these radio signals might enter the ionosphere and continue to propagate into the radiation belts in the form of whistler waves. Whistler-electron gyroresonance might then occur in the radiation belts and this could trigger some electrons to precipitate into the lower ionosphere, causing plasma line enhancement in the ionospheric E-region.
10

B
Whistler Wave - Electron
Gyroresonance kI
Arecibo ISR NAU
Figure 1-1: An illustration of a plausible scenario for the E-region plasma line enhancement observed over Arecibo.
In general, only a small portion of the transmitted VLF signals could be coupled into the ionosphere. The coupling efficiency can be estimated using the transmission coefficient from electromagnetic theory [1]. The transmission coefficient is given by the formula:
T 277p rp + rmo
(1.1) where 7p = V/E is the intrinsic impedance of the ionospheric plasma and 70 v/o/e is the intrinsic impedance of free space. The permeability of ionospheric plasma is not very different from that of free space, therefore we can assume / : o.
The permittivity of the ionospheric plasma in this case can be calculated using the dispersion relation for whistler waves (assuming parallel propagation): e e=
2
_ pe
W( Wce)
He
W W
(1.2)2 where pe, and w,,ce spectively. Whistler wave frequency in this case is 40.75 kHz, the electron gyrofrequency over Arecibo is approximately 1 MHz, and the typical electron plasma frequency in the ionosphere can be assumed to be 5 MHz. Substituting these numerical
11

values, we obtain r7p - 0.04 ro0.
It should also be noted that once these VLF waves (originally with linear polarization) enter the ionosphere, they will split into two circularly polarized EM waves.
One polarization component cannot propagate in the ionosphere and will be reflected back, whereas the other polarization component is the whistler wave that will continue to propagate into the radiation belts. Thus, we must remember to include a factor of 1/2 in calculating the coupling effeciency. The coupling efficiency will be the fraction of power that can penetrate the ionosphere:
PP
_lop
P
0
1
2
7/p p r
Up -rjo
)+ 0.075 (1.3)
Thus, only about 7.5% of the transmitted total power can be coupled into the ionosphere as whistler waves.
This coupling efficiency might be improved if there exist ducts or density irregularities in the ionosphere. The occurrence of spread F phenomena is a sign of the presence of ducts or density irregularities in the ionosphere. Ionospheric density irregularities can occur naturally and can also be generated artificially by transmitting
HF heater waves into the ionosphere. However, Arecibo Observatory currently does not have any heating facilities for us to operate. Thus, we were completely dependent on the natural spread F condition during our radar observation.
According to our hypothesis, E-region plasma line enhancement is caused by precipitated electrons from the radiation belts. While natural electron precipitation sometimes does occur, the injection of whistler waves into the radiation belts could trigger even more electrons to precipitate. Therefore, based on our hypothesis, we can list several factors that might affect the occurrence rate of E-region plasma line enhancement over Arecibo:
* NAU VLF transmitter at Aguada, PR. When NAU VLF trasmitter is on, whistler waves are being injected into the radiation belts and we might expect a more frequent E-region plasma line enhancement.
· Spread F condition. When spread F is very intense, it will be easier for
12

whistler waves to be coupled into the ionosphere. Therefore, there will be a higher chance for whistler-triggerred electron precipitation to occur and we might expect E-region plasma line enhancement to be more frequent.
The population of energetic electrons in the radiation belts. When energetic electron population is high, there will be a higher possibility for either natural electron precipitation or whistler-triggerred electron precipitation.
Thus, high electron population in the radiation belts might give us a more frequent E-region plasma line enhancement.
We are going to keep these possible controlling factors in mind when we examine the result of our observation of E-region plasma line enhancement over Arecibo later on in this thesis.
13

14

Langmuir waves are electrostatic plasma waves with frequency close to the local electron plasma, frequency. Indeed, in the case of unmagnetized plasma at zero temperature, Langmuir waves are reduced into non-propagating electron plasma oscillations at the electron plasma frequency. During plasma line measurements, we are using incoherent scatter radar to detect backscatter signal from Langmuir waves in the ionosphere that propagate in the opposite direction of the transmitted radar beam.
Since we are transmitting the radar beam vertically while the Earth's magnetic field over Arecibo is making an angle of - 45
° from the horizontal direction, the detected
Langmuir waves must be propagating at an angle of approximately 45
° with respect to the Earth's magnetic field. Thus, we are dealing with Langmuir waves that are propagating obliquely from the background magnetic field. In this chapter, we will derive the dispersion relation for oblique propagation of Langmuir waves in magnetized plasma and discuss the primary damping mechanism for these Langmuir waves.
15

We begin with the electron momentum equation: men ( a + [ ' v]) -en[f + v x Bo] - V[nkBT]
where n, v, F, T, me, kg, and Bo denote electron plasma density, electron velocity, electric field, electron temperature, electron mass, Boltzmann's constant, and background magnetic field, respectively.
Considering first order perturbations in n, v, and E; the electron momentum equation gives:
me(no + nl) a(k bi) +
[(
+ l) V](o +
1
vi) x o]- V[(no + nl)kB(To + T
1
)] (2.2)
In our analysis, we will assume the unperturbed velocity and the unperturbed electric field to be zero. After ignoring any second order terms in Equation 2.2, we obtain the linearized electron momentum equation:
(2.3) meno t -enoE
1
- enoe x Bo - kBToVnl - nokBVT
1
We will also assume adiabaticity,
v = constant z-
(2.4)
Combining the adiabaticity condition with the ideal gas law P = nkBT, we will find that
nqai l
VT = ( n o
(2.5)
After combining Equation 2.3 and Equation 2.5, we will simplify the linearized elec-
16

tron momentum equation into: air
=-noeE
1
- noel x
-
(2.6)
Similarly, we will also linearize the continuity equation:
(no + ni) + V [(no + n)(v + 1)] = 0 at at- +
Again, note that we have set the unperturbed electron velocity to be zero and ignored any second order terms.
We also need Gauss' law from Maxwell's equations to relate electron density perturbation to electric field perturbation:
V where e0 is the permitivity of free space.
.
e
Eo
(2.8)
We will now assume that all perturbing quantities are of the form eik
-i
t, so that we are allowed to make changes -iw and V --+ ik whenever these operators act on any perturbing quantity. In addition, we are going to choose a coordinate system where the background magnetic field Bo points along the + direction and the wavevector k lies in the xz plane, making an angle 0 with respect to the background magnetic field Bo. The geometry of this coordinate system is shown in Figure 2-1.
Furthermore, electrostatic wave characteristic (V x = 0) tells us that the wave electric field El is parallel to the wavevector k. More explicitly: Bo = [0, 0, Bo],
k = [k sin 0, 0, k cos 0], and El = [El sin 0, 0, El cos 0]. Hence, the linearized electron momentum equation, the linearized continuity equation, and Gauss' law can now be written explicitly as
17

x
A z Y
Bo
Figure 2-1: Geometry of the coordinate system for obliquely propagating Langmuir waves in magnetized plasma.
[
1
--iwmeno viy = -enoE
Vlz sin Vlvj o - enoBo -v
sin o cos
0
(2.9)
-iwn
1
+ inok(vi, sin 0 + vl, cos 9) = 0
CO
(2.10)
(2.11)
We are going to take the z-component of Equation 2.9 and use Equation 2.11 to substitute for El. Solving for vz in terms of nl:
-iwmenoVlz vlz
= -noe cos e
2
cok
- ik'ykBTonl cos 0 k-kBTo\ wmeok
W'IIkZkBo) wnm
Igm cos 0 nl
(2.12)
By using this result (Equation 2.12) to substitute for v1z in Equation 2.10, we can solve for vii in terms of n
1
:
Vx12 -
iwnl - inok cos 0 vlz
inok sin 0
)-[wnkos2 (2 ( e
nok sin
+ kkBTo)] n
18
(2.13)

We can now use Equation 2.13 to substitute for vl, in the y-component of Equation 2.9. Solving for vly in terms of nl:
V
1 y noeBovil
-'lwIIbel ,o ieBo
'
W te
[W-
nk cos
2
0 ( ek + kkTo
nok sin 0
(2.14)
And from Equation 2.11, we can certainly express E
1 in terms of nl:
E1 =-
eok
(2.15)
We will now take a scalar product between wavevector k and the linearized electron momentum equation:
k [-iwmI,no'iO = -enoEl - enoir x Bo - ikykBTonl ]
-iwmner[k vl] = -eno[k El] - erno[k' (vi x B
0
)] - ik
2
?ykBTonl
We will now examine all vector operations that appear in the above equation:
* From the linearized continuity Equation,
* From Gauss' law,
-
=-- ==
-
kl -- -
El t ienl no
* And finally,
k ( x Bo) = k - ( x )Bo = kBo [sin 0 0 lvy cos ] ·- v x ovl
Therefore, Equation 2.16 becomes ome
-
--2
-W ,
= k (v x Bo) = kBo sin vly
19
-nok ( eBo sin vly
\ rn
(2.17)
(2.16)

Furthermore, we can also simplify vly:
noi i nok nk cos 2 0 e2 + k-kBTo ZeBo
-nmEcos
2
(wE)k +nom wLme i (eBo' [
nok sin cos
2
0 ( n oe
2 nok me L w wmeo n k
2 ykBTO° ni wmine sin 0 i eBo 1 -Cos2
0 nok me 2
_ COs
2
Y kBTO/me nl
W
2/k2, sin 0 thermal speed phase
'elocity
)me/ eB- )n sin 0 sin
So, using Equation 2.17 and Equation 2.18, we obtain
(2.18)
2-Wn
=-i n
O e
2 come n
2 y
(kBTo m e
-
(eBo me
2 sin 2 0
For any nonzero perturbation nl to exist, we require w
2
2 t(noe 2
'\
+ yk
2
W2e
pe +
2
2
+ me me / sin
2
V
2
2= WpeA
D
D + We2, sin
2
0
W
2 e
Li(1 +
-y=
3
2 +w sin2 o
(2.19)
(2.20)
In the above expression,
Wpe is the electron plasma frequency, vte is the electron rms/thermal speed,
AD is the Debye length, and wce is the electron gyrofrequency. In addition, we have set y = 3 because the compression and the rarefaction of electrons are happening in one dimension only. In other words, this is a one dimensional adiabatic process and y = 3 for an adiabatic process with one degree of freedom [2].
Thus, we arrive at the dispersion relation for obliquely propagating Langmuir
20

waves in magnetized plasma,
2
= (1 + 3k22
) + W2 sin
2
0 (2.21)
In the case of parallel propagation ( = 0), the above expression will reduce into
Langmuir wave dispersion relation in unmagnetized plasma. On the other hand, in the case of perpendicular propagation ( = 7r/2), the above expression will give us the dispersion relation of the so-called upper hybrid waves.
Even in absence of collision in plasma, Langmuir waves will still experience damping.
This type of damping is referred to as Landau damping, in which electrostatic waves are damped due to energy transfer between waves and particles in the plasma. In the case of Langmuir waves, the waves primarily exchange energy with the electrons only.
Landau damping of Langmuir waves can be found by working out the dispersion relation for Langmuir waves using kinetic theory of plasma. For simplicity, we will consider the case of unmagnetized plasma and weak damping. We begin with Vlasov equation where we assume that particle acceleration is caused by the electric field only,
L + v Vf + Vv. f =
(2.22) where f denotes the distribution function of the particles for position (x, y, z) and velocity (vx, vy, vZ).
Assuming that Langmuir waves propagate in the -direction, we know that the electric field E will only have i-component and the spatial variation of f will consist of x-dependence only. Therefore, Vlasov equation will be reduced into:
Of
+ f
qE Of
+ n
f x
= O
21
(2.23)

We will now introduce a small perturbation in the distribution function so that we can write f = fo + fl. We will also assume that the equilibrium electric field is zero so that the electric field only has the perturbation term. In other words, E = El.
Linearizing Vlasov equation: afo at
+ at v- ax
+
+
1
Afo v
+ qEl afi m d v,
= O zeroth order zeroth order af1
+
0 (2.24) oaf qE
1
-
ax m avX
qEl fo m Ov
At
+
In obtaining the linearized Vlasov equation, we have thrown away zeroth order terms, neglected second order terms, and assumed e
- i wt+ikx dependence for the perturbing quantities. Rearranging terms in Equation 2.24, we have iqEl Ofo
(w - kvx)m avx
(2.25)
We can use Gauss' law from Maxwell's equations to relate the perturbation electric field with the perturbation in particle distribution:
V.E1
= -P
Co ikEl = q n
1 d3v
ikE
1
- q d3 v iqE
1 ao
E o (w kvx)m Ovx
0 = [+ ±d o2 (w/k-Vx) avoj
1
'
(2.26) where the integral will be over the whole 3-dimensional velocity space. For convenience, we will introduce equilibrium distribution function for particle velocity along the x-direction, f(vx), which can be defined through the relation: no f0I(v) = J|dvr dvz fo
22
(2.27)

Now one can see that
J Ofo-
(w/k - V') OvX
0
0 dv afO
(w/k-vx) avoo
(2.28)
Equation 2.26 has to hold for any arbitrary form of electric field perturbation El, therefore the quantity inside square bracket in Equation 2.26 has to vanish. Note that we are dealing with electrons so that q = -e and m is the electron mass. Thus, using Equation 2.28 and recognizing that w 2
_ 2, we obtain w
1+ 2e
2 r
1 Ofo d__ (w/k - vx) av o (2.29)
There will be some difficulty in performing the integration in Equation 2.29 because of a singularity at v = w/k. Contour integration will be used in dealing with this singularity because w will have a small positive imaginary part when collision is present.
We can show that w has a small positive imaginary part by introducing an effective collision frequency v. The collision frequency v will tend to stabilize any small perturbation by driving the particle distribution function toward the equilibrium distribution [3]. Therefore, from the Vlasov equation including the Krook collision term, a(f +
+ v
O(fo
At f tat
+ Vf + · Vvf = -v (f - fo) m
+ f) tOx
+ qE10(fo m avx
= fl
-iwfi + ikvxfi + qE fo
m v x iqEi 1 1 fo fi
-
mk (W
-
V) avX (2.30)
To evaluate the integral in Equation 2.29, we will use a deformed contour in the complex plane as shown in Figure 2-2. Basically, the integral will be equal to the
23

Im v x
V x
= oRlk
Re vr,
Figure 2-2: A deformed contour used in evaluating the integral that appeared in
Equation 2.29.
principal value plus a contribution from the pole. In the limit of e 0, r00 1 afo
Jdvx (w/k-v) 9v
}Vx d
00 kdv
1 fo 1 27ri Res [fo
0v,, 2
1 afo
Lv =k
(w/k-v.) 0vx dv fo(v,)
)
_
(,/k )2 fo o[
F
(v-)
w/-vx)
+e (/k-v) 2 vx = o =0 o fo(vz) fo
(w/k X) [0vxJ
] (2.31)
In the above manipulation, we have used the property that fo(vx) --* 0 as v --
+oo. We have also made an assumption that wlk > vt,, where vte is the electron rms/thermal speed associated with the velocity distribution function fo(vx). Consequently, fo(x) is negligibly small at v = wik.
With the assumption that w/k > Vte, we can further simplify Equation 2.31 by
24

making a Taylor series expansion:
00 dvz
-00
1 afo
(w'/k- v,) Ovx
-
0
0 0 ~ fo(v.)
(w/k- v)
l v =
I
Jf o(vz) d~z W (_ v~/_)2 i [aOfo k
2
2
J dv fo(v') 1
-00
2kvx w
-
3k2v~)
i
k
W
2
2
(1
+
2k(v~)
+
3k
2 k2
W2 ( 3k2v2 )
-
Vr
- i gfo
aV -Vx=
(2.32) where we have substituted (v,) = 0 and (v2) = v2e.
Therefore, from Equation 2.29 and Equation 2.32, we will have
w2
3kVe2e
W2
- VT-
Wk2
[afi]V
Ofo
=0
(2.33)
Rewriting Equation 2.33,
2
pe2
+ W,)pe
3k2vte
W2W 2 wk pe~ f
L9 V r
LI
(2.34)
In order to solve for w, which is assumed to be complex, we are going to write w = WRe + i WIm with WIJm WRe u 2
we + i 2
WReWlm. that in the lowest order, w 2 w
We also recognize plasma oscillations in cold plasma limit. Therefore,
WRe + i 2
WRe Wi
2
= Wpe +
2
WPe
2
;0W3pe
3k 2 v
2
'
W
2
+ i- W2 pe e afo0
19vz v.=LI
, k~k
(2.35)
25

Hence, by equating real and imaginary part separately, Equation 2.35 will give us w =w e + 3k ve2 (2.36a)
WIm 2 k
2
[3vfo 1 (2.36b)
The real part of the frequency gives back the Langmuir wave dispersion relation in the case of unmagnetized plasma, or parallel propagation of Langmuir waves in the case of magnetized plasma. On the other hand, the imaginary part of the frequency gives the damping/growth rate of Langmuir waves. When afo/Ov < 0, Langmuir wave will experience damping. Meanwhile, when fo/09v > 0, this corresponds to the growth of the wave.
26

A series of incoherent scatter radar (ISR) observation were carried out on several nights at the Arecibo Observatory from December 27, 2005 to January 3, 2006.
Plasma line measurements were taken twice every hour, where the duration of each plasma line measurement is approximately 10 minutes. For these measurements, the radar beam was transmitted vertically from the linefeed while the radar platform remained stationary throughout the experiment. In this experiment, coded-long-pulse technique was used to detect plasma line in the altitude range of 90 km to 495 km with a height resolution of 150 m. Specifically, we were recording plasma line spectra in the frequency-upshifted plasma line bandwidth (i.e., the downgoing Langmuir waves) between 2 MHz and 7 MHz.
In addition to the operation of ISR, an ionosonde and a VLF receiving system were also used to record data during the experiment. The ionosonde was mainly used to measure peak plasma frequency in the ionosphere and to monitor spread F condition, by recording ionograms once every 5 minutes. Meanwhile, the VLF receiving system was used to monitor radio signals from a nearby NAU VLF transmitter located at
Aguada, Puerto Rico.
27

31 December 2005. 03:31'48 LT 31 December 2005. 03:31:58 LT 31 December 2005. 03:32:08 LT
rrquecy uMnz) Preuency (MlnZ
Figure 3-1: An example of E-region plasma line enhancement event recorded in the early morning of December 31, 2005. The middle graph shows the enhanced plasma line spectra at 03:31:58 LT. Meanwhile, the leftmost and rightmost graphs show plasma line spectra recorded 10 seconds before and after the enhancement, respectively.
From this radar campaign, we found that plasma line enhancement was quite frequently observed in the E-region. The E-region plasma line enhancement was primarily observed as spiky bursts that last for a short period of time. The enhancement generally covers a quite broad altitude range, typically 50 km range centered around
125 km altitude.
An example of E-region plasma line enhancement events is shown in Figure 3-1.
The enhancement was observed within a 10-second integration time at 03:31:58 LT on December 31, 2005. Plasma line spectra recorded at 03:31:48 LT (10 seconds prior to the enhacement) and at 03:32:08 LT (10 seconds after the enhancement) did not show any sign of enhancement, as seen in the leftmost and the rightmost graph in
Figure 3-1. Thus, we can say that E-region plasma line enhancement over Arecibo typically lasts for less than 10 seconds.
In order to examine the strength of the enhancement, it is convenient to plot a part of the plasma line spectra from a specific altitude. Figure 3-2 shows two plots of plasma line spectra at an altitude of 124.7 km: the left plot is during the enhancement and the right plot is 10 seconds after the enhancement. In Figure 3-2, The size of the
E-region enhancement is shown on the left plot, while the size of noise level in the plasma line spectra is shown on the right plot. Based on the data shown in Figure 3-2,
28

x 10
n n~n1'
i=
-
I ' r I- L~
.
_
--
X 10" '4'"lI-'
.
_ .
I
- -tZ~n
IIUO. n-1 I .
O 7 m
. : Enhanced .3x10
16
5 5
4.5
4
-35
2
,_
2.5 3 3.5
.
, .
.
,,
4 4.5 5 5.5 6 6.5 7
4.5
4
3-5
? 5
---
3
Noise Level - 3x10'
5
' i
?,.i..i"' lW
I -
3 5
-
4
P, !I :
,
45 5 55 6 5 7
J
Figure 3-2: Left plot: enhanced E-region plasma line spectra at 124.7 km altitude, recorded in the early morning of December 31, 2005 at 03:31:58 LT. Right plot:
E-region plasma line spectra at the same altitude, recorded 10 seconds after the enhancement.
the noise level in the plasma line spectra is approximately 3 x 1015 (in arbitrary units) and the size of the enhanced signal is approximately 1.3 x 1016 (in arbitrary units).
This is an enhancement by a factor of - 4 in signal-to-noise ratio (SNR). Therefore,
E-region plasma line enhancement over Arecibo typically corresponds to an enhanced signal with SNR ~ 4, compared to the noise level with SNR 1.
The E-region plasma line enhancement is centered at 2.7 MHz in the frequency spectra, with frequency linewidth of
-
1.5 MHz. Based on this information, we can calculate the phase energy [4] of suprathermal electrons that were responsible for the excitation of Langmuir waves at this frequency range. Arecibo ISR is transmitting at frequency fR = 430 MHz, which corresponds to radar wavelength of
AR
= c/fR 70 cm. From the Bragg scattering condition, Arecibo ISR will detect Langmuir waves whose wavelength is equal to half of the radar wavelength. In other words, the detected Langmuir waves will have wavelength of A = AR/2 35 cm. Thus, the phase velocity of the detected Langmuir waves-which is equal to the speed of suprathermal electrons that excite these Langmuir waves-can be calculated as v = Af, where f is the Langmuir wave frequency inferred from the plasma line enhancement spectra. In this case. the Langmuir wave frequency ranges from -2 MHz to -3.5 MHz. The phase
29

energy of the suprathermal electrons can therefore be calculated using the formula [4]:
1
1
2 (3.1) where me is electron mass. Substituting numerical values, we obtained that the phase energy of the suprathermal electrons will range from -1.39 eV to -4.26 eV.
We suspect that E-region plasma line enhancement over Arecibo was caused by electrons that precipatate from the radiation belts into the lower ionosphere. Energetic electrons that precipitate from the radiation belts will eventually lose energy since these electrons will ionize atmospheric neutrals as they traverse through the
Earth's atmosphere. Given that the ionization energy for dominant neutral species in the Earth's atmosphere is in the order of -13 eV [5], the residual energy of these energetic electrons will be in the order of a few eV (i.e. below the typical ionization energy of -13 eV) when they reach the lower ionosphere. Thus, the value of electron phase energy (1.39 eV - 4.26 eV) that we calculated above is well within the typical range of the residual energy of precipitated electrons from the radiation belts. Therefore, the scenario of precipitated electrons from the radiation belts is a very plausible explanation for E-region plasma line enhancement over Arecibo.
In this section, we are going to highlight a few special cases of our ISR observations to elaborate some important trend of the E-region plasma line enhancement.
3.3.1 December 28 - December 29, 2005
Ionospheric condition during the night of December 28, 2005 until the morning of
December 29, 2005 was generally quiet, with a brief period of moderate spread F that quenched fairly quickly. Figure 3-3 shows a general overview of the E-region plasma line enhancement events and the value of what we define to be Spread F Index (See
Appendix A.2) throughout the radar observation.
30

3
E-Region Plasma Line Enhancement Events (Arecibo, 28,29 December 2005)
. _ I I
--
Plasma Line Measurement
(D
:>
-J
C
2.5
2
E o
C
1 c w
I1)
1.5
C
,1
E
2
(n
(U
1
0.5
-
0
.
J. L
00:00 02:00
Local Time
I
Spread F Strength at Arecibo. 28/29 December 20D5
Spread F Index
.
_j
_1
. I
06:00 C 4:00
2
1.8
1.6
1.4
1.2
l
...................
, .i .
i
I I
0.
0.
0.
O.
21:00 22:00 23:00 00:00 01:00 02
Local Time
2:00 03:00 04:00 05:00
Figure 3-3: Upper panel: A bar chart of E-region plasma line enhancement events recorded during the night of December 28, 2005 until the morning of December 29,
2005. Lower panel: Spread F Index during the radar observation.
06:00
31

From the upper panel of Figure 3-3, one can observe the trend of occurrence of
E-region plasma line enhancement during the night. Based on this data, it can be seen that E-region plasma line enhancement event has a higher rate after midnight than during the early evening. This observation provides us with an idea of general trend of occurrence of E-region plasma line enhancement when ionospheric condition is relatively stable throughout the night. Thus, we can so far conclude that electron precipitation rate tends to be low before midnight and gradually starts to increase after midnight.
Ionospheric condition during the night of January 1, 2006 until the morning of January
2, 2006 was quite active, with spread F that persisted for a relatively long time. The spread F strength, however, was fluctuating throughout the night. Figure 3-4 shows a general overview of the E-region plasma line enhancement events and the value of
Spread F Index throughout the night.
In the early evening of January 1, 2006, our observation using a VLF receiver showed that NAU 40.75 kHz radio signal was absent-indicating that NAU VLF transmitter was turned off at that time. However, starting at around 02:00 LT of
January 2, 2006, NAU 40.75 kHz radio signal finally appeared in the VLF receiving system-indicating that NAU VLF transmitter was turned on. Thus, with a period of NAU-off and another period of NAU-on, we had an opportunity to study the effect of injected whistler waves on the E-region plasma line enhancement over Arecibo.
As shown in Figure 3-4, the rate of E-region plasma line enhancement increased rapidly as soon as NAU VLF transmitter was turned on at around 02:00 LT. The clear difference in the enhancement rate between the period when NAU was turned off and the period when NAU was turned on had demonstrated the effect of the injected whistler waves on the E-region plasma line enhancement over Arecibo. When
NAU VLF transmitter was turned on, some of these VLF radio signals will propagate through the ionosphere in the form of whistler waves and eventually reach the radiation belts. Whistler waves can effectively interact with energetic electrons in
32

3
E-Region Plasma Line Enhancement Events (Arecibo. 12 January 2006)
Plasma Line Measurement -5 ci)
-J
C
2.5
2
E
0
C
C r-
1.5
1
E
U,
C a.
0.5
0
' -
22:00
LL~~
00:00
02:00
Local Time
1l
I1
04:00
NAU ON i V
06:00
21:00 22:00 23:00 00:00 01:00 02:00
Local Time
03:00 04:00 05:00 06:00
Figure 3-4: Upper panel: A bar chart of E-region plasma line enhancement events recorded (luring the night of January 1, 2006 until the morning of January 2, 2006.
Lower panel: Spread F Index during the radar observation.
33

the radiation belts. Energetic electrons that are originally trapped in the radiation belts can undergo pitch-angle-scattering when they are in resonant interaction with the whistler waves. As a result of this pitch-angle-scattering, trapped electrons whose pitch angle were close to the loss-cone angle could be scatterred into the loss-cone, causing these electrons to precipitate out of the radiation belts into the lower ionosphere.
Ionospheric condition during the night of January 2, 2006 until the morning of January
3, 2006 was more active than any of the previous nights. Spread F was relatively strong (with Spread F Index value of 1.5 or above during most part of the night) and persisted until around 03:30 LT early in the morning. Figure 3-5 shows a general overview of the E-region plasma line enhancement events and the value of Spread F
Index throughout the radar observation.
The data from January 2/3, 2006 was interesting due to the occurrence of especially strong spread F (with Spread F Index value of -2) at a certain period during the night (around 22:00 LT) and the occurrence of a sudden quenching of spread F in the early morning (around 02:00 LT). Thus, using this data, we could possibly identify the effect of spread F on the E-region plasma line enhancement over Arecibo.
In the period labelled A in Figure 3-5, spread F became very intense with Spread
F Index value approaching -2. At the same time, a few cases of E-region plasma line enhancement started to be observed while during plasma line mesurement just before and just after period A, no enhancement was observed. After all, period A happened prior to midnight, which-according to the trend observed from December
28/29, 2005-would typically contain very few or almost no E-region plasma line enhancement if quiet ionospheric condition were maintained.
Meanwhile, later during the night, a sudden quenching of spread F was observed around 02:00 LT (the period labelled B in Figure 3-5). Period B happened after midnight, which-according to the trend observed from December 28/29, 2005would correspond to the time when E-region plasma line enhancement starts to occur
34

3
E-Region Plasma Line Enhancement Events (Arecibo. 2. 3 January 2006) a
2.5
a)
(D
E a) o rC
2
1.5
(D
C
.i
E
1
I1
U)
0.5
o
11 .1..
22:00
_L
00:00 wl
Local Time
Plasma Line Measurement
02:00
B
11
Spread F Strength at Arecibo. 213 January 2006
Spread F Index
04:00
Li 1
I - I-9
06 ;:00
L
20:00 21:00 22:00 23:00 00:00 01:00 02:00 03:00
Local Time
04:00 05:00 06:00
Figure 3-5: Upper panel: A bar chart of E-region plasma line enhancement events recorded during the night of January 2, 2006 until the morning of January 3, 2006.
Lower panel: Spread F Index during the radar observation.
35

more frequently if stable ionospheric condition were maintained. Just before entering period B, we started to observe the after-midnight trend of a more frequent E-region plasma line enhancement. And indeed, long after period B had passed, the aftermidnight trend of a more frequent E-region plasma line enhancement was clearly seen.
Thus, the general after-midnight trend was still observed. It was only during period
B that we had a relatively sharp reduction of E-region plasma line enhancement rate immidiately after a sudden quenching of spread F.
This observation had demonstrated how spread F can possibly affect the occurrence rate of E-region plasma line enhancement over Arecibo. When spread F is strong, the coupling of whistler waves into the Earth's ionosphere will be stronger due to presence of ducts or density irregularities. Thus, strong spread F means a higher chance of having whistler waves interact with trapped electrons in the radiation belts, which will cause more precipitation. On the other hand, the coupling of whistler waves into the Earth's ionosphere is rather weak (7.5% of power transmission) in the absence of spread F. This would mean less chance of whistler-electron resonant interaction in the radiation belts, and consequently, less electron precipitation in general. Therefore, strengthening or weakening of spread F intensity could possibly drive the occurrence rate of E-region plasma line enhancement away from the general trend.
36

During a series of incoherent scatter radar experiments at Arecibo Observatory from
December 27, 2005 until January 3, 2006, we observed numerous events of plasma line enhancement in the ionospheric E-region. The E-region plasma line enhancement over Arecibo was primarily observed as spiky bursts that last for a very short period of time (in general less than 10 seconds). The frequency spectrum of the observed Eregion plasma line enhancement was found to be centered at 2.7 MHz with frequency linewidth of -1.5 MHz, which will correspond to electron phase energy that ranges from 1.39 eV to 4.26 eV. From our observation, we found that the occurrence rate of E-region plasma line enhancement tends to be higher after midnight. However, it was found that natural spread F condition could also affect this general trend. An intense spread F condition or a sudden quenching of spread F seemed to be able to influence the occurrence rate of E-region plasma line enhancement over Arecibo.
Finally, on one night of this radar campaign, we found a 4-hour period when NAU
VLF transmitter was turned off. As soon as NAU VLF transmitter was found to be on later that night, the occurrence rate of E-region plasma line enhancement was found to increase quite rapidly.
With these findings, we can now revisit our original hypothesis regarding E-region plasma line enhancement over Arecibo that we have stated in the beginning of this thesis. We hypothesized that E-region plasma line enhancement over Arecibo was caused by energetic electrons that precipitate from the radiation belts into the lower
37

ionosphere. The inferred value of electron phase energy that ranges from -1.39 eV to -4.26 eV supports this scenario very well. This is because the ionization energy of atmospheric neutrals is in the order of -13 eV and after a large number of impact ionization events, precipitating energetic electrons will eventually be left with residual energy just below this typical ionization energy (i.e. residual energy of a few eV).
Another fact that supports our hypothesis is the rapid increase of the occurrence rate of E-region plasma line enhancement when NAU VLF transmitter was turned on after being off for -4 hours. We knew that some (7.5%) of the transmitted power from NAU VLF transmitter can be coupled into the ionosphere, which will propagate into the radiation belts in the form of whistler waves. Whistler-electron gyroresonance interaction in the radiation belts can then trigger electron precipitation, exceeding its natural precipitation rate. Hence, this observation clearly demonstrated a link between the E-region plasma line enhancement and the precipitation of energetic electrons from the radiation belts. Furthermore, the fact that spread F condition also influenced the occurrence rate of E-region plasma line enhancement also provides an additional support for our hypothesis. This is because spread F is an indication of the presence of density irregularities in the ionosphere that might improve coupling efficiency of whistler waves to penetrate the ionosphere. Hence, if E-region plasma line enhancement over Arecibo had been caused by whistler-triggerred electron precipitation, its occurrence rate would have been dependent on the factor that controls this coupling efficiency.
Finally, although the occurrence rate of E-region plasma line over Arecibo generally obeys a certain trend, there are also variations from one night to another. This might be due to the influence of some other factors that are beyond our control. A possibility of these uncontrollable factors has already been stated in the beginning of this thesis: the population of energetic electrons in the radiation belts. The rate of either naturally-occurring or whistler-triggered electron precipitation will certainly be higher if the electron population in the radiation belts is high, and vice versa. Thus, for future studies, we probably also need to monitor electron population density in the radiation belts in order to clarify this portion of our observations.
38

In studying the ionosphere, one type of commonly used radio diagnostic instruments is a frequency-swept HF radar known as an ionosonde. An ionosonde sends highfrequency (HF) radio waves into the ionosphere and records the time delay for the transmitted radio wave to return. The time delay is often represented in terms of virtual height h, which is equal to the time delay At multiplied by c/2, where c is the speed of light in vacuum:
C
2
(A.1)
After the time delay for a pulse of radio waves with a certain frequency is recorded, the ionosonde will subsequently transmit another pulse of radio waves with an incremented frequency. An ionosonde typically scans frequency from 1 MHz to approximately 15 MHz, with a typical integration time of approximately 1 or 2 minutes.
The data from an ionosonde is commonly displayed in an ionogram, which is a plot of virtual height h versus frequency f. A schematic illustration of typical ionograms is depicted in Figure A-1.
In an ionogram, two types of backscatter traces are generally seen: O-mode and
X-mode traces. These refer to two different propagation modes of transverse electromagnetic waves in magnetized plasmas. These two propagation modes have different
39

h (km)
500
Typical Nighttime lonogram Traces
Typical Daytime lonogram Traces
220
6 11 f (MHz)
Figure A-1: An illustration of typical ionograms, showing the commonly observed
O-mode and X-mode ionogram traces recorded during nighttime and daytime.
cutoff frequencies and consequently, the reflection height of these two modes are different-the reflection height of the X-mode for a given frequency is lower than that of the O-mode. For either O-mode or X-mode propagation, ionosonde waves with frequency higher than a certain critical frequency will not be reflected back to the ground. Instead, waves with frequency higher than this critical frequency will continue to penetrate the ionosphere. The critical frequency for O-mode ionosonde waves is particularly important to us: this critical frequency corresponds to the peak plasma frequency in the ionosphere and is often referred to as the foF2. During the daytime, the value of foF2 is typically larger than the value of foF2 during the nighttime. This is understandable since during the daytime, solar UV radiation causes the ionization of neutrals and increases the ionospheric plasma density.
Occasionally, ionograms also show traces of backscatter signals that spread over a broad range of altitude-instead of clean and sharp traces. The appearance of spreading traces in the ionogram is referred to as the spread F phenomena, as the spread echoes are generally seen in the ionospheric F region. Typically observed during the nighttime, spread F is an indication of the existence of plasma turbulence
40

h (km)
,nn
Typical Nighttime
Ionogram Traces
U X:
Typical Daytime
Ionogram Traces
X
-------------
6 11 f(MHz)
Figure A-2: Another illustration of typical ionograms, this time showing the appearance of spread traces known as the spread F phenomena.
or the formation of density irregularities in ionosphere. Schematically, Figure A-2 illustrates how spread F phenomena are observed in an ionogram.
Spread F condition is an important phenomenon to monitor; yet, showing an array of more than ten ionograms in a single plot would be cumbersome. Thus, it would be convenient to summarize spread F condition during the experiment so that we can display it concisely together with other types of data for the purpose of data analysis or publications. One way to measure the strength of spread F is to assign an index for the intensity of spread echoes in an ionogram. This is analogous to the planetary
Kp index that measures the level of geomagnetic activity: the spread F index (SFI) will measure the level of turbulence of the local ionosphere.
The presence of spread F echoes implies more backscattered signals from the F region. Thus, when all signals from the F region are summed, strong spread F will give us a significantly higher total signal count compared to the quiet condition. As a first
41

step, we will integrate all ionosonde signals in the F region to obtain a preliminary measure of spread F strength:
-
( all backscattered
220 km < h < 500 km and f > 1.5 MHz
(A.2)
In the above expression, the height range is specifically chosen to isolate ionosonde signals from the F region and the lower limit of the frequency is intended to set up significant signal-to-noise ratio.
The next step is to normalize the raw total count using the raw total count from a quiet ionogram:
SFIRAW (quiet ionogram)
(A.3)
With this normalization, quiet ionograms with little or no spread F are set to have spread F index of approximately 1. In order to give a general idea on how spread F index works, a few sample ionograms with their respective spread F indices are shown in Figure A-3.
Dec 22, 2004 19:45:02
00
45
SFI= 1.00
.] i.'
5 0 0
Dec 26, 2004 20:10:02
.. SF 1.03
Dec 26, 2004 21:00:02
500 SFI= 2.45 .
:
450r i
0 r
450
Dec 26 2004, 22:45:02
450 i ,
IM
300 .' i
300'
00
200
2501. i .
.
I
50 '
1 2 3 4
FrlquMcy (MHz)
5 6
100,
1
2 3 4
F.qony (MHz)
5 6
1 5 0
L
1
F_010-y0 (MHZ)
6
?250:
150i 'a H
.*x
A. L
2 3 4
Frequpy (MHz)
I -
5 6
Figure A-3: Sample ionograms with their respective spread F indices. The leftmost ionogram is a standard quiet ionogram chosen for normalization purposes. The subsequent ionograms show how spread F index increases as spread F echoes become stronger.
Finally, we will give an example of a plausible practical use of the spread F index to summarize spread F condition over a certain period. This is shown in Figure A-4,
42

3.'
3
A
Spread F Strength at Arecibo. 26 December 2004
Spread F Index (SFI)
0.
1
Local Time
Figure A-4: A plot of spread F index as a function of time,
F region activity on December 26, 2004.
summarizing ionospheric where we summarize spread F condition for the entire day of December 26, 2004. After sunset on December 26, 2004, ionospheric condition was generally quiet but starting by the presence of spread F. From the SFI plot, one can see the time development of spread F condition relatively more easily, as the data presentation is simplified.
43

44

[1] MIT ASIS/IRIS group, research discussion at Arecibo Observatory (August 2005).
[2] D.R. Nicholson, Introduction to Plasma Theory (John Wiley & Sons, 1983).
[3] F.F. Chen, Introduction to Plasma Physics and Controlled Fusion, 2nd Ed.
(Plenum Press, New York, 1984).
[4] H.C. Carlson, V.B. Wickwar and G.P. Mantas, Observations of Fluxes of
Suprathermal Electrons Accelerated by HF Excited Instabilities, Journal of Atmospheric and Terrestrial Physics 44, 12 (1982).
[5] Y. Kim, Electron-Impact Cross Sections for Ionization and Excitation, National
Institute of Standards and Technology, Atomic Physics Division,
(http://physics.nist.gov/PhysRefData/lonization/molTable.html).
45