Impact of dust particulates on hall thruster

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IMPACT OF DUST PARTICULATES ON HALL THRUSTER

JASVENDRA TYAGI

DEPARTMENT OF PHYSICS

INDIAN INSTITUTE OF TECHNOLOGY DELHI

SEPTEMBER 2019

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©Indian Institute of Technology Delhi (IITD), New Delhi, 2019

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IMPACT OF DUST PARTICULATES ON HALL THRUSTER

by

JASVENDRA TYAGI Department of Physics

Submitted

in fulfilment of the requirements of the degree of Doctor of Philosophy

to the

Indian Institute of Technology Delhi

September 2019

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Dedicated to

my respected parents and guruji

&

those

whoever inspired and encouraged me

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Certificate

This is to certify that the thesis entitled “Impact of Dust Particulates on Hall Thruster” being submitted by Mr. Jasvendra Tyagi to the Department of Physics, Indian Institute of Technology Delhi is worthy of consideration for the award of the degree of Doctor of Philosophy and is a record of the original bonafide research work carried out by him under my guidance and supervision, and that the results contained in it have not been submitted in part or full to any other university or institute for award of any degree/ diploma.

I certify that he has pursued the prescribed course of research. I approve the thesis for the award of the degree of Doctor of Philosophy.

Hitendra K. Malik Professor Department of Physics Indian Institute of Technology Delhi INDIA

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Acknowledgements

During the course of Ph.D. at IIT Delhi, I have been blessed with the support of many people.

First and foremost, I would like to express my deep and sincere gratitude to my supervisor Professor Hitendra K. Malik for providing me opportunity to work with him and for his advice, patience, support and guidance during this entire duration of the course. His insights remain always enlightening to me. His guidance and support motivated me to complete my research.It was truly a pleasure working with him and I am going to miss my interactions with him. The time I spent with him and his group is the most exciting and precious experience in my career. His expertise, enthusiasm and positive outlook on research and life in general have been of great value for me. Thank you for providing me the opportunity to get involved in such an exciting field. I cannot list my thanks to him because they are actually uncountable.

My thanks and appreciations go to my SRC members, Prof. B. D. Gupta, Prof. P.

Senthilkumaran and Prof. B. S. Panwar for their constructive inputs at various stages.

I would like to thank all my seniors and lab-mates of Plasma Waves and Particle Acceleration (PWAPA) Laboratory of Department of Physics, IIT Delhi, for endless hours of useful discussions and their supports.

Above all, I extend many thanks to my parents, my wife Priyanka Tyagi, my sister Dr.

Kalpana Tyagi, brother-in-law Mr. Pankaj Kumar Tyagi and brother Yogendra Tyagi for their support and encouragement during the course of Ph.D. research. I would like to express love to my daughter Srishti, son Atharav and nephew Siddhant. I have been able to complete this journey due to the blessings of my mother Late Urmila Tyagi. Also, I wish to pay special thanks to my father Sh. Mangesh Kumar Tyagi who has always taught me to do my best and be strong in all matters of life.

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At last but not the least, I express my gratitude to God for providing me the strength and patience to complete the quality research work for my Ph.D. thesis and blessing me with lot of friends and wonderful family.

Jasvendra Tyagi

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Abstract

A Hall thruster (HT) is a popular electric propulsion device rather than chemical thruster, which provides continuous thrust while maintaining high efficiency and propellant utilization. In a typical Hall thruster, the propellant is injected inside the channel from the anode. The electrons are trapped in an annular channel due to azimuthal E B

 drift. When neutral particles are injected from the anode, they encounter the region of high electron density and hence, the ionization occurs due to the collisions. Thus, the newly born unmagnetized ions accelerate axially out of the thruster channel due to the electrostatic potential maintained between the anode and external cathode. However, during the operation of the Hall thruster, the oscillations grow in the plasma due to density gradient, nonuniform magnetic field, collisions between the plasma species, etc. Hence, different types of instabilities occur in the thruster that affect the operation of Hall thruster. On the other hand, in a Hall thruster, the ions and the electrons collide with the walls of the chamber that generate dust particulates in the thruster plasma. These dust particulates affect the process of operation and hence the efficiency of Hall thrusters is expected to lower.

In the thesis, two types of instabilities, namely resistive instability and Rayleigh–

Taylor (RT) instability, have been studied in the presence of dust particulates. The impact of dust particulates on resistive instability have been examined. Specifically the resistive instability has been studied under the following three cases. At first, the calculations have been done by neglecting the dust temperature and dust drift velocity; the dispersion equation is obtained and solved numerically for examining the growth rate. Then in the next part, resistive instability is studied under the temperature of dust, in the situation of strongly tilted waves along axial direction. Finally, the ionization is also taken into account and cumbersome problem is solved for obtaining the dispersion equation. The effects of dust density, dust charge

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number, dust mass, dust temperature, collision frequency of electrons with neutrals, drift velocity, magnetic field, axial and azimuthal wave numbers are studied in greater detail on the growth of resistive instability. In the next part of the thesis, RT instability has been studied.

Since the RT instability mainly develops due to the density gradient, the role of different density profiles, electron drift velocity profiles and ionization has been studied. It has been shown that the growth rate of this instability is not so sensitive to the drift velocity profile but it varies significantly for the different density profiles. In view of the occurrence of the dust near the exit, we have taken the distribution of the dust density such that it stays maximum towards the exit of the chamber and the densities of ions, electrons are maximum in the middle of the chamber. A frequency band for the oscillations of the waves has been found in the Hall thruster plasma. This frequency band gives the lower cutoff frequency and upper cutoff frequency of the oscillations. The results show that the frequency band is very narrow towards the anode side in the channel; however, the width of the frequency band increases after the middle of the chamber towards the exit. Thus, the waves having higher frequency or smaller wavelength oscillations are found to be more unstable towards the channel exit.

The overall conclusion is that the RT and resistive instabilities are sensitive to the contaminated plasma parameters of the Hall thrusters.

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सार

हॉल प्रक्षेपक रासायनिक प्रक्षेपक के बदले एक लोकप्रप्रय वैद्युत प्रणोदि युक्ति है, जो

उच्च दक्षिा और प्रणोदक उपयोग को बिाए रखते हुए निरंतर प्रक्षेप प्रदाि करता है। एक प्रवशिष्ट हॉल प्रक्षेपक में, प्रणोदक को एिोड से चैिल के अंदर इंजेक्ट ककया जाता है। ददगंशीय बहाव के

कारण इलेक्रॉि एक कुंडलाकार चैिल में रैप्ड हैं। जब उदासीन कणों को एिोड से इंजेक्ट ककया

जाता है, तो वे उच्च इलेक्रॉि घित्व के क्षेत्र का सामिा करते हैं और इसशलए टकराव के कारण आयिीकरण होता है। इस प्रकार नए उत्पन्ि अिमैग्िेटाइज्ड आयि एिोड और बाहरी कैथोड के

बीच बिी इलेक्रोस्टैटटक पोटेंशियल के कारण प्रक्षेपक चैिल से अक्षीय रूप से बाहर निकलते हैं।

हालांकक हॉल प्रक्षेपक के संचालि के दौराि घित्व के ढाल, असमान चुंबकीय क्षेत्र, प्लाज्मा स्पीिीज के बीच टकराव, आटद के कारण प्लाज्मा में दोलिों का प्रवकास होता है। इसशलए प्रक्षेपक में

प्रवशिन्ि प्रकार की अस्स्थरताएं होती हैं जो हॉल प्रक्षेपक के संचालि को प्रिाप्रवत करती हैं। दूसरी

ओर, हॉल प्रक्षेपक में आयि और इलेक्रॉि चैंबर की दीवारों से टकराते हैं जो प्रक्षेपक के अंदर प्लाज्मा में धूशलत कण उत्पन्ि करते हैं। ये धूशलत कण संचालि की प्रकिया को प्रिाप्रवत करते

हैं और इसशलए हॉल प्रक्षेपक की दक्षिा कम होिे की उम्मीद है।

थीशसस में दो प्रकार की अस्स्थरताएं, अथाात ् प्रतिरोधी अस्स्थरता और रेले-टेलर (आरटी) अस्स्थरता का धूशलत कणों की उपस्स्थनत में अध्ययि ककया गया है। प्रतिरोधी अस्स्थरता पर धूशलत कणों के प्रिाव की जांच की गई है। प्रविेष रूप से निम्िशलखखत तीि मामलों के तहत प्रतिरोधी अस्स्थरता का अध्ययि ककया गया है। सबसे पहले, धूशलत कणों के तापमाि और इनके

बहाव के वेग की उपेक्षा करके गणिा की गई है; ववकास दर की जांच के शलए, डडस्पेरिि समीकरण संख्यात्मक रूप से प्राप्त और हल ककया जाता है। उसके पश्चात ् धूशलत कणों के तापमाि के तहत प्रतिरोधी अस्स्थरता का अध्ययि ककया जाता है, जो अक्षीय टदिा के साथ काफी झुकी तरंगों की

स्स्थनत में होती है। अंत में, आयिीकरण को िी ध्याि में रखा जाता है और डडस्पेरिि समीकरण प्राप्त करिे के शलए कदिन समस्या को हल ककया जाता है। प्रतिरोधी अस्स्थरता की वृप्रि पर धूशलत कणों के घित्व, धूल के आवेश िंबर, धूल द्रव्यमाि, उदासीन कणों के साथ इलेक्रॉिों की

टकराव आवृस्त्त, बहाव वेग, चुंबकीय क्षेत्र, अक्षीय और ददगंशीय तरंग संख्या के प्रिावों का अधधक प्रवस्तार से अध्ययि ककया जाता है। थीशसस के अगले िाग में, आरटी अस्स्थरता का अध्ययि

ककया गया है। चूंकक आरटी अस्स्थरता मुख्य रूप से घित्व के ढाल के कारण प्रवकशसत होती है, इसशलए प्रवशिन्ि घित्व के पाश्वाधचत्र, इलेक्रॉि बहाव वेग के पाश्वाधचत्र और आयिीकरण की

िूशमका का अध्ययि ककया गया है। यह टदखाया गया है कक इस अस्स्थरता की ववकास दर बहाव वेग के पाश्वाधचत्र के प्रनत इतिी संवेदििील िहीं है, लेककि यह प्रवशिन्ि घित्व के पाश्वाधचत्र के

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शलए महत्वपूणा रूप से शिन्ि है। हॉल प्रक्षेपक के तनकास के निकट धूशलत कणों की घटिा को

देखते हुए, हमिे धूल के घित्व का प्रवतरण इस तरह ककया है कक यह चैम्बर के तनकास की ओर अधधकतम रहता है और चैम्बर के बीच में आयिों िथा इलेक्रॉिों का घित्व अधधकतम होता है।

हॉल प्रक्षेपक के प्लाज्मा में तरंगों के दोलिों के शलए एक आवृस्त्त बैंड पाया गया है। यह आवृस्त्त बैंड निम्ितम कटऑफ आवृस्त्त और दोलिों की ऊपरी कटऑफ आवृस्त्त देता है। पररणाम बताते

हैं कक आवृस्त्त बैंड चैिल में एिोड की ओर बहुत संकीणा है; हालााँकक आवृस्त्त बैंड की चौडाई चैम्बर के मध्य से तनकास की ओर बढ़ जाती है। इस प्रकार, उच्च आवृस्त्त या छोटे तरंग दैध्या दोलि

वाले तरंगों को चैिल के तनकास की ओर अधधक अस्स्थर पाया जाता है।

समग्र निष्कषा यह है कक आरटी और प्रतिरोधी अस्स्थरताएं हॉल प्रक्षेपक के दूविि प्लाज्मा

के मापदंडों के प्रनत संवेदििील हैं।

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(

Dust Temperature T_d 0 and Dust Drift Velocity _d₀ 0) 27

2.2. Dispersion Equation 29

2.3. Results and Discussions 32

2.3.1. Resonance of wave with Ions Drift 38 2.4. Limiting Cases 39

Chapter 3: Tilted Resistive Instability in Hall Thruster 43 – 52 3.1. Model and Fluid Basic Equations 43

3.2. Results: Numerical solution of Dispersion Equation 47

3.3. Growth Rate: Analytical Calculations 50

Chapter 4: Role of Ionization to Resistive Instability in Hall Thruster 53 – 70 4.1. Plasma Model and Basic Fluid Equations 53

4.2. Results and Discussion: Growth Rate and Phase Velocity 57

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4.3. Discussion on Limiting Case: In the Absence of Dust and Low Temperature 66 4.4. Special Case: Analytical Growth Rate of Instability (when k_x k_y) 68

Chapter 5: Contribution of Dust Particulates to Rayleigh–Taylor Instability 71 – 88 in a Hall Thruster

5.1. Derivation of Modified Rayleigh Equation 71

5.2. Conditions for Rayleigh Instability: Frequency Band 76

5.4. Dispersion Equation and Growth Rate Analysis 83

Chapter6: Rayleigh–Taylor Instability under Various Profiles of Density 89 – 108 and Velocity of Plasma Species

6.1. Model of Hall Plasma with Dust 89

6.2. Dispersion Equation in the Absence of Collisions 92

6.3. Results with Their Discussion 94

6.4. Condition for Rayleigh Instability 106

Chapter7: Rayleigh–Taylor Instability under the Effect of Ionization 109 – 120

7.1. Model of Hall Plasma with Dust 109

7.2. Dispersion Equation 112

7.3. Results and Discussion 114

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7.4. Condition for Rayleigh Instability: Perturbed Part of the Equation 118

Chapter 8: Conclusions and Future Prospects 121 – 126

8.1. Resistive Instability 121

8.1.1. Absence of Temperature and Drift of Dust Particles 122 8.1.2. Tilted Resistive Instability (k_x k_y) 122

8.1.3 Effect of Ionization 123

8.2. Rayleigh–Taylor Instability 123

8.2.1. Effect of Maximum Dust Density at the Exit of Chamber 124 8.2.2. Effect of Different Density and Electron Drift Velocity Profiles 125

8.2.3. Effect of Plasma Ionization 126

8.3. Future Prospective 126

References 127 – 134

List of Publications 135 – 138

Brief Bio-data of Author 139

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List of Figures

Fig.1.1. A typical Hall plasma thruster’s schematic diagram.

Fig.1.2. Profile shape of the radial magnetic field B_rand axial electric fieldE_x.

Fig.1.3. Schematic of a) Stationary Plasma Thruster (SPT) and b) Thruster with Anode Layer (TAL).

Fig.1.4. Functional diagram of a typical hollow cathode.

Fig.2.1. Variation of the growth rate  with the dust density for different values of dust mass and dust charge number in a plasma having Xeions (M = 131 amu), when T_e 25eV, T_i 1 eV, n_i₀ 10¹⁸/m³, B0.015T, k_y 400/m, k_x 20/m, _i₀ 10⁴m/s, _e₀ 10⁶m/s, Y_e 

i 

Y 2, V_thi 1.210³m/s, V_the310⁶m/s, 4.410⁹/s and v10⁶/s.

Fig.2.2. Variation of growth rate  with azimuthal wave number for different values of dust density, when m_d 10^²³kg, Z_d 100 and the other parameters are the same as in Fig.2.1.

Fig.2.3. Variation of the growth rate  with the collision frequency for different values of the dust charge, when m_d 10^²³kg, n_d₀ 10¹³/m³ and the other parameters are the same as in Fig.2.1.

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Fig.2.4. Variation of phase velocity with azimuthal wave number for different dust density, when m_d 10^²³kg, Z_d 100and other parameters are the same as in Fig.2.1.

Fig.2.5. Variation of real frequency with azimuthal wave number for different dust mass and dust charge number when n_d₀10¹³/m³ and other parameters are the same as in Fig.2.1.

Fig.3.1. Variation of the growth rate  with the dust charge for different the dust density in the plasma having Xe ions (M=131amu), when B0.015T, T_e 25eV, T_i 1eV, eV, n_i₀ 10¹⁸/m³, /m³, , _e₀ 10⁶m/s, m/s,

0 10

d m/s, /m, = kg, cm and /s.

Fig.3.2. Variation of the growth rate  with the dust density for different magnetic fields in the plasma having Xeions (M = 131amu), = 500 and all other parameters are same as Fig. 3.1.

Fig.4.1. Variation of the growth rate  with the dust charge number with different density of dust in the plasma having Xe ions (M = 131amu), when B0.015T, T_e 25eV, T_i 1eV,

03 .

0

Td eV, n_i₀ 10¹⁸/m³, n_e₀ 110¹⁸m³, _i₀ 10⁴m/s, _e₀ 10⁶m/s, _d₀ 10m/s,

500

ky /m, k_x 10/m,  10⁵/s and v_e 10⁶/s.

Fig.4.2. Dependence of the growth rate  on the dust density and the mass of the dust particles, when Z_d 100 and the other parameters are the same as in Fig.4.1.

Zd

03 .

0

Td n_d₀ 10¹⁴ n_e₀ n_i₀Z_dn_d₀ _i₀ 10⁴

x 

k k_y 1000 m_d 10^¹⁷ d 6.0 v10⁶

0

nd

Zd

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Fig.4.3. Dependence of the growth rate  on the ionization rate for different values of Z_d and the cases of k_x k_y 354/m (solid line), k_x k_y, k_x= 10/m and k_y= 500/m (dashed line).

Other parameters are the same as in Fig.4.1 except n_d₀ 0.00110¹⁸/ m³.

Fig.4.4. Variation of the growth rate  with the magnetic field in the plasma for the case

y

x k

k  , k_x= 10/m and k_y= 500/m (dashed line) and k_x k_y 354/m (solid line). When

100

Zd , n_d₀ 0.00110¹⁸/m³ and other parameters are the same as in Fig. 4.1.

Fig.4.5. Variation of the growth rate  with the collision frequencyv_e, when B0.015T and the other parameters are the same as in Fig.4.1.

Fig.4.6. Dependence of the growth rate  (solid lines) and the phase velocity (dotted lines) on the azimuthal wave number (k_y), when B0.015T and the other parameters are the same as in Fig. 4.1.

Fig.4.7. Dependence of the growth rate  (solid lines) and the phase velocity (dotted lines) on the axial wave number (k_x), when B0.015T and the other parameters are the same as in Fig.4.1.

Fig.5.1. Electron density and density gradient profiles.

Fig.5.2. Electron velocity and velocity second derivative profiles.

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Fig.5.3. Variation of the cutoff frequency



_cutoff with the axial distance

x

in the plasma having Xe ions (M = 131amu), when B0.010T, Z_d= 800, T_e 20eV, T_d 0.01eV, n_i₀ 10¹⁸/m³,

13

0 5 10

nd   /m³, n_e₀ n_i₀Z_dn_d₀, _e₀ 10⁵m/s, _i₀ 10⁴m/s, m_d = 10^²⁵ kg, k_y 400/m,

e 

Y Y_i Y_d  2 and d 7.0cm.



_cutoff with the dust density n_d₀ for different masses of the dust particles in the plasma having Xe ions, when the other parameters are the same as in Fig. 5.3.



_cutoff with the electron density n_e₀ for the different dust charge number and electron temperature in the plasma having Xe ions and when the other parameters are the same as in Fig. 5.3.



_cutoff with the magnetic field B for different the density of ions in the plasma having Xe ions and when the other parameters are the same as in Fig. 5.3.

Fig.5.7. Growth rate versus the dust density for the different masses of the dust particles in the plasma having Xe ions (M = 131amu), when T, = 1000, eV,

eV, /m³, , m/s, m/s, /m,

and cm.

Fig.5.8. Growth rate versus the dust charge number in the plasma having Xe ions, when

 n_d₀

0 0.015

B  Z_d T_e 25

03 .

0

Td n_i₀ 10¹⁸ n_e₀ n_i₀Z_dn_d₀ _e₀ 10⁶ _i₀ 10⁴ k_y 100 Y_e 

i d

Y Y  2 d 5.0

 Z_d

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= kg, /m³, /m, cm and all the other parameters are the same as in Fig. 5.7.

Fig.5.9. Growth rate versus the dust temperature for the different dust charges in the

plasma having Xe ions, when = kg, /m³, /m, cm and

all other parameters are the same as in Fig. 5.7.

Fig.5.10. Growth rate versus the azimuthal wave number for the different dust density and the channel length ( ) in the plasma having Xe ions, when = kg and all the other parameters are the same as in Fig. 5.7.

Fig.6.1. Density distribution of all three species (the ion, the electron and the dust) as

mentioned above Profile 1 (solid), Profile 2 (dashed), Profile 3 (dashed-dotted) and Profile 4 (dotted).

Fig.6.2. Super-Gaussian Profile (SGP) and Step-Like Profile (SLP) for the electron drift velocity.

Fig.6.3. Variation of the growth rate  with the magnetic field B for the different density profile 1 (solid) and profile 4 (dotted) in the plasma having Xe ions (M = 131 amu) when

20

Te eV, T_i 1eV, T_d 0.03eV, n_i₀ 10¹⁸/m³, n_d₀  1 10¹⁴/m³, n_e₀ n_i₀Z_dn_d₀,k_y 400 /m, Z_d 10 ,³ _i₀ 10⁴m/s, _e₀ 10⁶m/s, _d₀ 10 m/s, m_d = 10^²¹kg, Y_e = Y_i = Y_d = 2, ₁= 16, and d 6.0cm.

md 10^²⁰ n_d₀ 5 10¹⁴ k_y 1000 d 6.0

 T_d

md 10^²⁰ n_d₀  5 10¹⁴ k_y 1000 d 6.0

 ky

d m_d 10^²⁰

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xv

Fig.6.4. Variation of the growth rate  with the dust density n_d for the different density profiles, when B = 0.010 Tand the other parameters are the same as in Fig.6.3.

Fig.6.5. Variation of the growth rate _ with the density profile factor ₁ for the different density profiles, when B = 0.010 Tand other parameters are the same as in Fig.6.3.

Fig.6.6. Variation of the growth rate _ with the dust charge number Z_d in the presence of different density profiles, when B = 0.010 T and the other parameters are the same as in Fig.6.3.

Fig.6.7. Variation of the growth rate  with the temperature of dust T_d in the presence of the different density profiles, when B = 0.010 T and the other parameters are the same as in Fig.6.3.

Fig.6.8. Variation of the growth rate _ with the electron drift velocity _e₀ for the different density profiles, when B = 0.010 T and the other parameters of the plasma are the same as in Fig.6.3.

Fig.6.9. Variation of the growth rate  with the magnetic field for the density profile 1 under super-Gaussian profile (dotted) and step-like profile (solid) of electron drift velocity, when the parameters are the same as in Fig.6.3.

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xvi

Fig.6.10. Variation of the growth rate _ with the channel length d for the density profile 1 under super-Gaussian profile (dotted) and step-like profile (solid) of electron drift velocity when B = 0.010 T and the other parameters are the same as in Fig.6.3.

Fig.6.11. Variation of the growth rate _ with the azimuthal wave number k_y with density profile 1 under super-Gaussian profile (solid) and step-like profile (dashed) of electron drift velocity when B = 0.010 T and the other parameters are the same as in Fig.6.3.

Fig.7.1. Variation of the growth rate  with the ionization rate  for the different dust particles mass in the plasma having Xe ions (M = 131 amu) when T_e 20eV, T_i 1eV, T_d 0.03eV,

18 0 10

ni /m³, n_d₀  1 10¹⁴/m³, n_e₀ n_i₀Z_dn_d₀,k_y 600/m, Z_d 10 ,³ _i₀ 10⁴m/s,

6 0 10

e m/s, _d₀ 10 m/s, m_d = 10^¹⁷kg, Y_e = Y_i = Y_d = 2 and d6.0cm.

Fig.7.2. Variation of the growth rate  with the magnetic field B for the different dust charge number, when  10⁵/sand other parameters are the same as in Fig.7.1.

Fig.7.3. Variation of the growth rate  with azimuthal wave number k_y for the different electron temperatures, when  10⁵/s and other plasma parameters are the same as in Fig.7.1.

Fig.7.4. Variation of the growth rate  with dust temperature T_d for the different density profile factor, when  10⁵/s and the other plasma parameters are the same as in Fig.7.1.

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xvii

List of tables

Table. 2.1. Variation of tilt angle and phase velocity with azimuthal wave number.

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xviii

Nomenclature

B

: External static magnetic field applied in the z-direction



Bzˆ



E

: Electric field

0: Permittivity of free space c : Speed of light

d : Channel length e : Charge of electron

T: Total efficiency



: Growth rate of the wave k : Wave number

kx: Axial wave number ky: Azimuthal wave number

L : Inhomogeneity length along the channel mi: Mass of the ion

me: Mass of the electron md: Mass of the dust ni: Density of the ion ne: Density of the electron nd: Density of the dust

ve: Collision momentum transfer frequency between the electrons and neutral atoms

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xix

 : Electron cyclotron frequency

pi: Ion plasma frequency

pe: Electron plasma frequency

pd: Dust plasma frequency

LHF: Lower hybrid frequency

cutoff

 : Cutoff frequency of oscillation

Real: Real frequency of the wave V_ : Phase velocity of the wave

pi: Ion pressure pe: Electron pressure pd: Dust pressure

: Plasma potential

r

: Radius of thruster channel Ti: Temperature of the ion Te: Temperature of the electron Td: Temperature of the dust

0

i : Unperturbed ion fluid velocity

0

e : Unperturbed electron fluid velocity

0

d : Unperturbed dust fluid velocity

i : Fluid velocity of the ion

e : Fluid velocity of the electron

d : Fluid velocity of the dust

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xx VthI: Ion thermal velocity

VthE: Electron thermal velocity VthD: Dust thermal velocity

: Ionization rate

x: Axial distance in the channel Yi: Specific heat ratio for the ion fluid Ye: Specific heat ratio for the electron fluid Yd: Specific heat ratio for the dust fluid

Impact of dust particulates on hall thruster

IMPACT OF DUST PARTICULATES ON HALL THRUSTER

JASVENDRA TYAGI

DEPARTMENT OF PHYSICS

INDIAN INSTITUTE OF TECHNOLOGY DELHI

SEPTEMBER 2019

IMPACT OF DUST PARTICULATES ON HALL THRUSTER

by

JASVENDRA TYAGI Department of Physics

Submitted

in fulfilment of the requirements of the degree of Doctor of Philosophy

to the

Indian Institute of Technology Delhi

September 2019

Dedicated to

my respected parents and guruji

&

those

whoever inspired and encouraged me

Certificate

Acknowledgements

Abstract

Table of Contents

(

List of Figures



x







List of tables

Nomenclature





r