令和元年度
九州大学大学院 総合理工学府
先端エネルギー理工学専攻

修 士 論 文論文名
ThrustPerformance

Dependency

On

Propellant

Characteristic of Ablation-Fed Pulsed Plasma Thruster

氏

名

齊木 淳

指導教員名

山本 直嗣

II

CONTENT ·························································································Ⅲ
CHAPTER 1: INTRODUCTION ······························································· 1
1.1 WHAT IS THE ELECTRIC PROPULSION ·············································· 11.2. RESEARCH BACKGROUND ····························································· 2
1.3. THE OBJECTIVE OF THIS RESEARCH ··············································· 41.4. PULSED PLASMA THRUSTER ·························································· 4
1.5. PPT TYPES···················································································· 7
1.6. PPT MODELS ················································································ 8
1.6.1. THE MODEL APPLYING LCR CIRCUIT ············································ 8
1.6.2. THE MODEL APPLYING MHD THEORY ········································· 15
1.6.3. THE MODEL APPLYING ELECTROTHERMAL ACCELERATION·········· 18
CHAPTER 2: EXPERIMENTAL EQUIPMENT ··········································· 20
2.1. EXPERIMENT SYSTEM ································································· 20
2.2. MEASUREMENT AND CONTROL EQUIPMENT ································· 21
2.2.1. THRUST SIGNAL RECEIVER AND IGNITER SIGNAL GENERATOR ····· 22
2.2.2. ROGOWSKI COIL ······································································ 22
2.2.3. DISCHARGE CURRENT AND VOLTAGE WAVEFORM MEASUREMENT 26
2.3. POWER SUPPLY ·········································································· 27
2.3.1. POWER SUPPLY FOR PPT···························································· 27
2.3.2. IGNITER MODULE ····································································· 27
2.4. THRUST MEASURING SYSTEM······················································ 29
2.4.1 THRUSTER STAND ····································································· 29
2.4.2 CALIBRATION ··········································································· 30
2.5. VACUUM SYSTEM ······································································· 33
2.6. HIGH SPEED CAMERA (FASTCAM SA-Z) ········································· 35
CHAPTER 3: PERFORATED SOLID PROPELLANT VERIFICATION ·············· 36
3.1. LABORATORY PPT ······································································· 36
3.2. NORMAL SHAPE SOLID PROPELLANT TEST ·································· 37
3.2.1 NORMAL SHAPE PTFE SOLID PROPELLANT EXPERIMENT ·············· 37
3.2.2 RESULT AND DISCUSSION ·························································· 40
3.3. PERFORATED SOLID PROPELLANT TEST ········································ 45
III3.3.1 PERFORATED SOLID PROPELLANT ·············································· 45
3.3.2 PERFORATED SOLID PROPELLANT RESULT AND DISCUSSION ········· 46
3.3.3 COMPARISON OF PERFORATED AND NORMAL SHAPE SOLID
PROPELLANT············································································ 49
CHAPTER 4: CONCLUSION ································································· 54
REFERENCES ··················································································· 56
ACKNOWLEDGEMENTS ···································································· 59

IVChapter 1: Introduction
In this chapter, the brief introduction concerning the background research and researchbackground and the motivation of the thesis will be presented. The literature review will be conductedin order to explain the main concepts presented in this paper.

1.1.

What is the electric propulsion?

In general, the propulsion unit is normally the chemical rocket engine which is installed on launchvehicle. The thrust of chemical propulsion unit is generated due to the increasing enthalpy per unit
time caused by the burning fuels and oxidants. Different from the chemical propulsion unit, the electric
propulsion unit generates a thrust due to the electric power such as electrothermal, electromagnetic
and electrostatic. The limitations of available thrust of chemical propulsion are dependent on specificchemical energy of the fuel. In contrast, the electric propulsion unit can generate thrust unlimitedly
according to the supply power theoretically. The primary characteristic differences of both propulsions
are summarized in Table 1.1. Due to their different characteristics, the chemical propulsion is normallyapplied to launch vehicle, and electric propulsion is applied to satellite.
Table 1.1. Differences of chemical and electric propulsion units

ChemicalElectric

Thrust per unit time

High

Low

Thrust efficiency

Low

High

Propulsion unit is basically evaluated by specific impulse Isp or momentum coupling coefficient
Cm. The specific impulse is basically applied to the evaluation of propulsion unit that can generate
steady thrust for supply power. It is defined as

𝑰sp =

𝒗
∫ 𝒇𝑑𝑡
=
𝐠𝑜 ∫ 𝑚̇𝑑𝑡 𝐠𝑜(1.1)

where f is thrust, 𝑚̇ is mass flow rate of exhaust, v is velocity of exhaust, go is gravitational
acceleration at sea level[1]. In this equation, specific impulse indicates that the thrust per unit
consumed propellant mass. Propulsion units with unsteady thrust for supply power, which can control
the mass flow rate and supply power separately, or cannot control feed required amount of propellant,
are evaluated by momentum coupling coefficient. It is defined as

̇ 𝑑𝑡
∫ 𝑚𝒗

𝐶𝑚 = 𝐸

𝑠𝑢𝑝𝑝𝑙𝑦1=𝐸𝑚𝒗

𝑠𝑢𝑝𝑝𝑙𝑦(1.2)

where mv is impulse bit of exhaust, Esupply is supply energy. In the other word, momentum coupling
coefficient show the quantity of unit supply energy that can varies the motion trajectory.
The detail of the target propulsion unit type in this research will be described later part, it cannot
control the consumed mass amount precisely due to the propellant supply principle. Furthermore, thisthruster generates momentary thrust and generally evaluated in impulse bit. Therefore, momentum
coupling coefficient is applied as basic evaluation item in this thesis.

1.2. Research backgroundIn recent years, the global interest in space development is increased. In particular, with the rapid
development of communication technology, it attracts attention of private enterprises in terms of
constructing a communication network. For example, OneWeb LLC which is a global
communications company in USA plans to connect the globe by approximately 600 low orbital (at1200 km altitude) satellites in coming ten years [1]. One suitable technology for such demands is thesmall satellite which is defined as the satellite with a net weight less than 500 kg. The appeal of thistype of satellite is the low cost of development and launch. Although available missions are limited
compared with the large artificial satellites, the development period and cost can be reduced because
the required technical hurdles are relatively low. Thus the cost can reduced by launching with otherartificial satellites such as the piggyback satellite [5].
The core technology in the small satellites development is the small propulsion unit that is called
the micro-thruster. The requirements of this thruster include the following four elements:
1. Light weight and miniaturization easiness
2. Low consumption of electrical energy (less than several hundred W )3. Wide thrust range which can correspond from the attitude control to the orbital transition
4. High specific thrust and propulsion efficiency
Normally, a satellites equipped with two types of propulsion units for attitude control and orbitaltransition separately. However, a small satellite cannot load multiple propulsion units due to the weightand volume limits. Therefore, the propulsion unit must achieve both functions as slated in (3). The
final requirement presented in (4) is an indispensable condition for effective acceleration due to the
reducing power source weight and propellant weight[6].
The propulsion unit of a space craft can be implemented by either electric and chemical types.
The chemical propulsion unit can generate a strong thrust, but its specific thrust is low. Therefore, it
is normally applied in the short period mission such as launch vehicle. But the electric propulsion unit
is a high specific thrust even with a tiny thrust which is suitable as a micro-thruster. The specific thrustof the electric propulsion unit can exceed 1000 s, while the specific thrust of the cold gas jet that has
been used as an attitude control propulsion unit for satellite is approximately several 10 s. For example,
the gas jet thruster of PROCYON which is an ultra-small satellite for deep space exploration
2

(developed by Intelligent Space System Laboratory, The University of Tokyo) can generate only 24 s
specific thrust [7]. Thus the electric propulsion shows great advantages on its thrust performance.
However, the electric propulsion system must be required scale down. But the thruster performance isalso going down as the size scaled down. For example, the arc jet thruster can work with low powersuch as less than 100 W. But if the output power is 400 W or less, thrust performance decrease sharply[8].
“Pulsed Plasma Thruster (PPT)” is one of the most promising candidate electric thrusters as
micro-thruster with less than 100 W power consumption. In an amount of previous works, PPTs
normally use solid propellants and generate plasma by the propellant sublimation by pulsed arc
discharge. And the plasma is then accelerated electromagnetically or electrothermally. The solid
propellant PPT is called Ablative Pulsed Plasma Thruster (APPT) since the solid propellant in it issupplied to the discharge room by ablation process ignited by the arc discharge. In addition, by thesimple structure of a APPT, is easy to be minimized and scaled down in size and weight.
However, there are still a number of limitations a real-word APPT operation. One primary
defect is their low efficiency (typically less than 10 % [9]. Poor propellant utilization due to thegeneration of heavy neutral mass is the major reason identified for this low efficiency. The majormechanism of generating heavy neutral mass is the Late Time Ablation (LTA). LTA is the process ofthe solid propellant sublimation from the consumed surface after plasma generation, which is causedby the radiation of generated plasma [11]. Since the gas is neutral, which is non-conductive, it cannot
promote thrust because it cannot be accelerated by the electromagnetic force. The gas is then ejected
due to the tiny force caused by the increased enthalpy. The primary limitation of LTA is that the almost
component of consumed mass is that neutral gas. As an example, in the propulsion unit of the Lincoln
12 Experimental Satellite (LES-6), the charge accumulation in the Faraday cup shows that the ionized
mass is only approximately 1 µg of the total 10 µg, indicating an extremely low efficiency of thepropellant.[12]The second limitation factor is the contamination of exhausted gases. The typical propellant of
the APPT is the Polytetrafluoroethylene (PTFE) as solid propellant based on an amount of previous
studies [1]. Since PTFE is a polymer including C2F4 as a monomer, PPT exhaust contains atoms andcompounds consisting of carbon and fluorine. Since the chemical reactivity of fluorine is strong, thenegative effect to solar cells and other optical equipment is considerable[17]. Meanwhile, the chemical
reactivity of carbon is relatively weak, but the light transmissions to solar cells and other opticalequipment are blocked due to the generated carbon particles. In addition, if the carbon particles
absorbed and deposited between the electrodes, it may cause the PPT malfunction due to the shortcircuit between various eletrodes.
The third limitation factor is the uneven consumption of a solid propellant. If APPT is operated
for a long period, a solid propellant can be consumed unevenly thus form an irregular surface which
also causes malfunction or decreasing efficiency. Furthermore, since a solid propellant usually can not
be consumed completely, the extra propellant load is required in APPT which causes increase ofweight and size.
31.3. The objective of this research
In this research, we try to find that how much effect can be seen on ablative pulsed plasma thruster
performance by changing the solid propellant shape.
The reason of changing propellant shape is as following.
The first one is to reduce the consume propellant mass. Almost propellant mass is consumed andwasted by the heat transfer of radiation from generated plasma to solid propellant surface. The shapeof APPT solid propellant is commonly simple form such as rectangle or cylinder. If solid propellant
is processed such as making holes for the consumed surface of solid propellant and increasing theentire surface area, the radiation intensity also be reduced by dispersing the radiation energy due tosuppress the temperature rise on the solid propellant surface which is the aim of changing shape. Since
PPT can be generate only unstable plasma, estimating the accurate radiation amount is difficult.
Therefore, in this research, we estimate the consumed mass of processed solid propellant by assumingthat radiation is irradiated uniformly to entire surface in hall. In the other words, we assume that thepropellant surface area of radiation irradiated is simply expanded. Since that area is expanded,radiation intensity will be decreased and wasted mass is also decreased.
The second reason is to verify the relation of solid propellant shape and impulse bit or consumed
mass. If this relation is shown, the ideal shape of solid propellant might exist. To measure the impulse
bit, we made thruster stand what can measure the tiny force in µNs order.
However, if the solid propellant surface density is decreased by perforating on consumed
propellant surface, the impulse bits generated by PPT are expected to decrease naturally because thesupplied propellant mass should be decreased also. If solid propellant is assumed to consumed
uniformly, the impulse bit will be reduced according the density of solid propellant surface.

1.4. Pulsed Plasma Thruster
In this section, the propulsion characteristics and principle of the ablation-fed pulsed plasma
thruster generally abbreviated as PPT is reviewed. PPT is a one of the non-stationary operationelectromagnetic acceleration type electric thruster for satellites. Of all the various electric propulsion
concepts, because of its system simplicity, the APPT was the first to realize acceptance for propulsion
unit on space missions. Decades later, the demand of PPT was followed by the other type electrical
propulsion unit such as the xenon ion engine, the stationary plasma thruster (SPT), expanded hydrazine
thruster, and the arc jet thruster. On the other hand, in contrast with a moment operation propulsion
unit as the PPT, these steady-state propulsions optimized their performance levels after development
for a lot of years. In fact, the thrust efficiency of SPT-100, that is one kind of a hall-effect ion thruster,and the xenon ion engine achieved 50 %. However, in spite of a much lower efficiency, the PPT wasapplied the selection for space craft applications in the 1960s because of the low cost, robustness,
simplicity and short development period. Since the PPT placed on thus unique position which is notcomparable simply with other thruster, there is considerable opportunity to be mounted to a satellite,4however, in same time, it is facing a lot of improvement, especially efficiency [6].
A lot of types of PPT exist depending on electrode shape or solid propellant supplying method.
Figure 1.1 displays one kind of the PPT, which is most traditional type, breech-fed, rectangularelectrodes, driven by an LCR (inductance-resistance-capacitance) pulse circuit. Usuallypolytetrafluoroethylene(PTFE) is applied as a solid propellant bar which is installed into the gap
between two electrodes. The principle of PPT is as follows:
1. The main capacitor connected to two electrodes is charged at 1-3 kV in vacuum.
2.

An igniter generates small amount of initial plasma due to the sublimation of propellant
bar around igniter, triggering a radiation energy of electrical discharge across the
exposed surface of the solid propellant bar.

3. The initial plasma is grown up and extended between two electrodes due to the electricenergy and fields of charged capacitor.
4. Since the discharging circuit is closed by extended plasma, the charge in capacitor isreleased and causes main discharge. At that same time, propellant is supplied moreover
to discharge chamber by heart transfer from generated plasma.
5. The generated plasma is accelerated by electromagnetic forces due to the self-induced
magnetic field from electrodes and pressure forces.
6. Finally, the accelerated propellant is ejected to downstream direction with expanding
discharge area, and the propulsion unit obtains a thrust by this reaction.
7. As the propellant is consumed at each discharge, the propellant bar is pushed axiallyinto the discharge chamber with a simple spring mechanism. It contributes to eliminate
the complex system such as a propellant tank or feed control device.
A lot of type of the PPT exist such as the “side-fed” type (Figure 1.2) or the coaxial arrangement(Figure 1.3). The side-fed PPT is supplied two propellant bars from lateral of discharge chamber.

Extrusion spring

Igniter

CathodeSolid propellant
Anode
Figure 1.1. Breech fed rectangular type APPTThis type can be applied in rectangular or coaxial electrodes. The coaxial PPT was originallydeveloped as the magnetoplasmadynamic (MPD) thruster, and is member of PPT because of5

similarity to PPT in principle.
The systems case for the PPT was considered by Palumbo and Guman based on approximately
for 9000 h of PPT operations on LES-6 which is one of the satellite over a10-year period beginningin 1968, and the character of PPT was reported as a satellite propulsion unit by them as follows:
1) Do not need warmup time and standby power.
2) No complex mechanism and fail-safe.
3) Easy to fit to requirements of mission.
4) Usable on stabilization of satellites.
5) Advantages of solid propellant: no tank, feedlines, mechanical valves and seals, easy tomeasure propellant consumption, stability of propellant for temperature or storage
period, nontoxic, vacuum compatible, or robustness for variable high “g” loads.
6) Compatible with digital logic because of impulse bits.
7) Available wide range thrust by operating frequency.
8) Satisfying two function of attitude control and orbital transition.
9) Capability for variable temperature of environmental.
In addition, the PPT is suitable to the mission requiring a fine position and attitude control ofsatellites such as formation flying which is required high accuracy of positioning capability.
Furthermore, the design with robustness can correspond to immediate operation, even after waiting
for a lot of year. These advantages show the reason that the PPT was initially hired on satellite, anddevelopment is being continued today.

1.5. PPT Types
As shown in Table 1.1, PPT can be classified to four types depending on this shapeand feed mechanism.
Table 1.2. PPT types
Electrode configuration

Rectangular

CoaxialFeeding method

Breech-fed

Side-fed

The oldest and basic structure of the PPT is the parallel rectangular electrodes withbreech-fed type which is driven by a pulse current. This type PPT is represented as the
LES-8/9 or EO-1 propulsion unit. The current and self-induced magnetic field for therectangular electrode configuration are generated primarily transverse to the exhausting
direction. The arc discharge attachment regions on the anode and cathode move todownstream along the electrodes with the plasma flow.
The configuration of coaxial type usually hires the conical shape, and typically loads the cylinder
solid propellant and two cylinder electrodes in central and downstream as shown in Figure 1.3. The
igniter plug in any PPT is usually inserted on the cathode because the negative charge electrons6discharged from igniter are not absorbed to the electrode and irradiated to the solid propellant surface.
In the coaxial type, it can be installed either the downstream or the center electrode. The outer cylinder
electrode is usually narrow, so that the current inserted at a definite location. Diffident values ofmagnetic Reynolds number result in a limited downstream extension depend on current patterns.
Igniter

CathodeExtrusion spring

Solid propellant

Solid propellant

Anode

Figure 1.2. Side-fed rectangular type APPT

Igniter
Extrusion spring

Anode

Solid propellant

CathodeFigure 1.3. Coaxial type PPTWhether the PPT is breech-fed or side-fed, the operation mode of PPT is the ablation arc or
7

propagating. These two operating modes are closely similar to deflagration and propagating modes in
the PPT with electromagnetic type also using gas injection.

1.6. PPT models
Basically, the PPT obtains thrust by the Lorentz force which is generated between
the self-induced magnetic field and the discharge current. That is, this thruster uses thatthe loop current including plasma receives a force to the out ward direction of the loop
due to interact this current and self-induced magnet field.

1.6.1. The model applying LCR circuit
The plasma in PPT is contracted and formed as sheet due to the pinch effect, whichis called“current sheet”. PPT can be modeled as shown in Figure 1.4. The Lorentz force FEM
received by current sheet at position x can be obtained by integrating the Lorentz force j
× B per unit volume with the volume of the current sheet𝒙+𝜹

𝑭𝐄𝐌 = ∫𝒙𝒉𝒅

∫ ∫ 𝒋 × 𝑩𝒅𝒙𝒅𝒚𝒅𝒛
𝟎(𝟏. 𝟑)

𝟎where j is current density, B is magnetic flux density.
If electromagnetic acceleration wants to be written accurately, there is necessary to

Figure 1.4. The electromagnetic model of PPT[13], V(t): Voltage between electrodes, B:
Magnetic flux of self-induced magnet field, J(t): Discharge current, h: Gaps between
electrodes, d: Electrode width,

δ: Thickness of current sheet
8

apply MPD theory, however, a formulation or a calculation are extremely complex.
Therefore, it come often as an electrical circuit concept by being assumed that a circuitcomposed of capacitors and electrodes is consisted of lumped constant system. As Figure
1.4, the capacitor with capacitance C is assumed that be charged initial voltage Vo. whena tiny discharge induced by igniter, the circuit is closed by generated plasma, then, an arc
discharge occurs. Ro is defined the entire circuit resistance immediately after plasma
generation and L0 is inductance. Since the plasma moves to downstream due to theLorentz force caused by discharge current, the area of the circuit loop increases with time.
Therefore, the inductance L(t) at an arbitrary time t is a monotonically increasing function.
This rectangular circuit is applied Maxwell law[13]

𝛁×𝑬=−

𝜕𝑩
𝜕𝑡

(1.4)

Area integral along current path∫ (𝛁 × 𝑬) ∙ 𝑑𝐴 = − ∫𝑆𝑆

𝜕𝑩𝑑𝐴 = −𝝋̇𝜕𝑡(1.5)

where S is an area formed by the loop circuit, A is its area vector, φ is magnetic flux whichis interlinking the area of the loop. Here, the Stokes’ theorem is given with Γ that is a loop
passing through the edge of area S∮ 𝑬 ∙ 𝑑𝑠 = ∫ (𝛁 × 𝑬) ∙ 𝑑𝐴
𝛤

(1.6)

𝑆

Then, this equation is applied to left side of equation (1.5)∮ 𝑬 ∙ 𝑑𝑠 = −𝝋̇

(1.7)

𝛤

The relation of any electric field Ea and potential Va is given as

𝑉𝑎 = − ∫ 𝑬𝑎 𝑑𝑠(1.8)

Therefore, the equation (1.7) can be shown as follows with the voltage V between
electrodes9(1.9)−𝑉 + 𝑱𝑅 = −𝝋̇Furthermore, it is transformed as
𝑉 = 𝑱𝑅 + 𝝋̇
𝑑
(𝐿𝑱)
𝑑𝑡
= 𝑱𝑅 + 𝐿𝑱̇ + 𝑱𝐿̇
= 𝑱𝑅 +(1.10)

Since V is also charging voltage of capacitor, this equation can be transformed as

𝑱𝑅 + 𝐿𝑱̇ + 𝑱𝐿̇ + 𝑉0 −1 𝑡
∫ 𝑱𝑑𝑡 = 0
𝐶 0

(1.11)In the other hand, the equation of motion of current sheet is given as𝑑(𝑚𝑥̇ ) = 𝑭𝐸𝑀
𝑑𝑡(1.12)

FEM is already expressed by equation (1.3), however, it can also be described with thespatial gradient of the electrode inductance

𝑭𝐸𝑀 =

𝛁𝐿 2
𝑱
2

(1.13)

By the equation (1.11) – equation (1.13), the motion of current sheet can be described.
However, the modeling for process of propellant supply should be required because thismodel does not include it. As the major model, there are “Slug model” and “Snowplow
model”. Slug model is assumed that all propellant for one operation is supplied at thesame time as the discharge starts. That is, it can be described as m(t) = m0,where m0 iscurrent sheet at t = 0. Snowplow model is the idea that current sheet mass increase due tothe sheet absorbing ambient gas while the sheet is going to downstream. In this case, thecurrent sheet mass m(t) is given as𝑡𝑚(𝑡) = 𝑚0 + ∫ 𝜌(𝑥)𝑥̇ 𝑑𝑡(1.14)

0where ρ(x) is the gas density at position x. If the gas density is constant in discharge
channel, above equation can be described as10

(1.15)𝑚(𝑥) = 𝑚0 + ℎ𝑑𝜌𝑥

For improving performance of PPT, it is necessary to consider about efficiency relational
expression between the initial inductance L0 and the inductance increase ΔL due to thecurrent sheet moving. By the multiplying both sides of equation (1.10) by current J, thesupplied power from capacitor to circuit can be foundP = 𝐉V = 𝑱𝟐 𝑅 + 𝐿𝑱
= 𝑱𝟐 𝑅 +𝑑𝑱+ 𝑱𝟐 𝐿̇𝑑𝑡

𝑑 1 𝟐
1( 𝐿𝑱 ) + 𝐿̇𝑱𝟐
𝑑𝑡 2
2

(1.16)In this equation, the first term is equivalent to Joule heating per unit time, the second term
is varying energy over time, the third term shows the consumed power for current sheettransfer, in other word, the power of electromagnetic acceleration. By the integral this Pwith time, the energy amount W0 supplied from the capacitor can be expressed as𝜏

𝑊0 = ∫ 𝑃𝑑𝑡0𝜏= ∫ (𝑱2 𝑅 +
0
𝜏

𝑑 1 𝟐
1
( 𝐿𝑱 ) + 𝐿̇𝑱𝟐 ) 𝑑𝑡
𝑑𝑡 2
2

1
= ∫ (𝑱2 𝑅 + 𝐿̇𝑱2 ) 𝑑𝑡
20(1.17)

1
Since J2 is in common term of R and 2 𝐿̇, 𝐿̇ is identical dimension of R. The energy ratio

ηe of the charged energy in capacitor and consumed energy for electromagnetic
acceleration is defined as𝜏

1 ∫0 𝑱2 𝐿̇𝑑𝑡
𝜂𝑒 =
2 𝑊0

(1.18)

However, it is assumed that the energy of electromagnetic acceleration gained bypropellant is not lost and is completely converted to physical energy. To estimate orderof ηe, the current amplitude value J0 with following condition is applied・Zero resistance of circuit
・The entire circuit inductance is fixed initial value L0
・The discharge current is a sine wave with amplitude J0
11

The above condition cannot be realized naturally, these are just reference value for
estimation of efficiency ηe. In this case, the charged energy W0 in capacitor equals the1charged energy 2 𝐿0 𝑉02 in inductor
1
𝑊0 = 𝐿0 𝑣02
2(1.19)

Equation (1.19) and (1.18) are combined as𝜂𝑒 =𝜏
∫0 𝑱2 𝐿̇𝑑𝑡

(1.20)

𝐿0 𝐼02

Due to the inductance monotonous increase with time, and resistance R is a finite value,
J < J0. Therefore, the efficiency ηe is given by𝜏𝜂𝑒 =∫0 𝑱𝟐 𝐿̇𝑑𝑡
𝐿0 𝐼02

𝜏<∫0 𝑱𝟐𝟎 𝐿̇𝑑𝑡
𝐽02 𝐿0=∆𝐿
𝐿0(1.21)

𝜏
where ΔL equals ∫0 𝐿̇𝑑𝑡 , which means the increase of inductance amount due to thecurrent sheet moving to downstream. From the above equation, the PPT performance
depends on the initial inductance L0 and the increase of inductance amount ΔL due to thecurrent sheet moving. Since the inductance is known as that it is decided by the shapecondition as electrode width, length or gaps, the initial inductance L0 depends on the shapeof circuit and the increase of inductance amount ΔL depends on shape of electrode. This
fact indicates that when we design the PPT, we must to care the shape of electrode or
feedthrough.
To make it easy, by the applying electric charge Q with assumption that eachparameter L and R in the discharge circuit are constant, the following second order linear
differential equation is given
𝑄=0𝐶
𝑄(0) = 𝐶𝑉0

𝐿0 𝑞̈ + 𝑅0 𝑄̇ +(1.22)(1.23)𝑄̇ (0) = −𝑱(0) = 0
If the above equation is solved and assigned to following equation, V(t) and J(t) is
obtained12𝐉 = −𝑄̇(1.24)

𝑄
𝐶(1.25)𝐉=

The analytical solution of equation (1.24) can be classified into the following three types
according to value of C𝑅02 /4𝐿0 which depends on L, C and R. When C𝑅02 /4𝐿0 < 1, itis the inadequate damping waveform, and the waveform of current and voltage aredescribed as
𝑉

𝐶

𝑅

0

0

𝑉 = 𝜔0 √𝐿 𝑒𝑥𝑝 (− (2𝐿 ) 𝑡) sin(𝜔𝑡 + 𝛿 )𝑱=𝑉0𝑅
𝑒𝑥𝑝 (− () 𝑡) sin(𝜔𝑡)
𝐿0 𝜔
2𝐿0

(1.26)(1.27)

where ω and δ are
1

1
𝑅02 2
ω=(
−
)
𝐿0 𝐶 4𝐿20(1.28)
1

2
4𝐿0
δ = 𝑡𝑎𝑛−1 ( 2 − 1)
𝑅0 𝐶

(1.29)In the case of C𝑅02 /4𝐿0 = 1, the waveform is critical damping

𝑉 = 𝐶𝑉0 (1 +
𝑱=

𝑅0
𝑅0
𝑡) exp(−
𝑡)
2𝐿0
2𝐿0

𝑉0
𝑅
exp (− (
) 𝑡)
𝐿0
2𝐿0

(1.30)(1.31)In the case of C𝑅02 /4𝐿0 > 1, the waveform is overdamping
𝑉

𝐶

𝑅

0

0

𝑉 = 𝜔′0 √𝐿 𝑒𝑥𝑝 (− (2𝐿 ) 𝑡) sinh(𝜔′𝑡 + 𝛿′)𝑱=𝑉0𝑅
𝑒𝑥𝑝 (− () 𝑡) sinh(𝜔′𝑡)
𝐿0 𝜔′
2𝐿0

13

(1.32)(1.33)

where ω’ and δ’ are
1

𝑅02
1 2
′
ω =( 2−) = 𝑖𝜔
4𝐿0 𝐿0 𝐶(1.34)

1

4𝐿0 2
δ′ = tanh−1 (1 − 2 )𝑅0 𝐶(1.35)In a real PPT, the capacitor inductance or the inductance between electrodes are at least
10 nH, and the capacitance of the capacitor is approximately 100 µF at most. Therefore,
the current or voltage waveform are usually the inadequate damping because of
C𝑅02 /4𝐿0 < 1. Since L0 and R0 are important parameters that affect PPT performance,
the equation to find the entire inductance L and the entire resistance R should be derived
from discharge current and voltage waveforms. To make it easy, the equation (1.27) canbe described as following with the logarithmic decay rate α and angular frequency ω
𝑱 = 𝑱𝑎 exp(−𝛼𝑡) sin(𝜔𝑡)𝜔=√(1.36)

1
𝑅2
− 2
𝐿𝐶 4𝐿

(1.37)

𝑅
4𝐿(1.38)

𝛼=The ratio of time tpeak at the maximum current and the current after one period is given by𝑱(𝑡peak )𝑱(𝑡peak + 𝑇)=

𝑱𝑎 exp(−𝛼𝑡peak )𝑱𝑎 exp(−𝛼𝑡peak + 𝑇)

(1.39)

where T is one period shown as T=2π/ω. By the applying natural logarithm of both sidesof above equation, the logarithm decay ratio is described as
𝑱(𝑡

𝛼=

)

ln (𝑱(𝑡 peak+𝑇))
peak𝑇

L and R can be expressed by α

14

(1.40)

𝐿=
𝑅=

1
𝐶(𝜔 2 + 𝛼 2 )2𝛼𝐶(𝜔 2 + 𝛼 2 )(1.41)(1.42)

Therefore, L and R can be calculated by assigning each value of the peak current and its
time to the equation (1.40) – (1.42). Incidentally, this calculation is possible with the
waveform of discharge voltage.

1.6.2. The model applying MHD theory
In this subsection, the relation of the energy of PPT, mass shot and impulse bit isdescribed by the ideal MHD model which is application of MHD theory with quasistationary and one dimension. If the PPT discharge is assumed that the discharge type isquasi-steady mode, the discharge is kept at propellant surface. Quasi-steady mode is oneof the condition that conductive particles always stay at propellant surface by a sufficientheat transfer from the generated plasma to propellant. Under the quasi-steady condition,
the magnetic Reynolds number is less than 1, which means that the generated plasma isfrozen on magnetic fields. In addition, if the ratio β of a pressure and a magnetic fieldpressure is small enough and the gas dynamic effect can be ignored, the condition ofmagnetic sound velocity can be satisfied because PPT inject to free vacuum. Therefore,
following equation at magnetic sound velocity can be described as𝒖∗= 𝑽𝐴∗ =

𝑩∗√μ𝜌∗

(1.43)

where u is a flow velocity, VA is a partial Alfven velocity, ρ is a density and B is a magnetic
flux density. “*” means that it is the value at the point of magnetic sound velocity. The
magnetic flux density at a propellant surface of the rectangular electrodes channel backside is given by

𝑩0 =

μ𝑱
𝑑

(1.44)

where J is an entire discharge current, d is a width of an electrode. In addition, if the mass
flow rate per unit area on the rectangular cross section as Figure 1.4 is expressed as 𝜔 =𝑚̇/𝑑ℎ, the equation of continuity, the physics equation, the energy equation are given by𝜌𝒖𝑑ℎ = 𝑚̇15(1.45)

𝜌𝒖 = 𝒋𝑩𝑧

(1.46)

𝑚̇
𝐸𝑩0 𝑚̇
𝒖2
𝐸𝑩ℎ0 +=(ℎ + ) +
𝑑ℎ
μ
𝑑ℎ
2
𝝁

(1.47)

where 𝑚̇ is a mass flow rate of propellant, E is an electric field strength which is uniform
in channel, h is specific enthalpy. Since the gas dynamic pressure can be ignored becauseof low B, the pressure gradient term is deleted from equation (1.47). If Hall effect isignored, j is described as follows by ampere’s circuital law

𝒋=

1 𝑑𝑩𝑧
μ 𝑑𝑥

(1.48)In the case with the extended Ohm's law, j is expressed as
𝒋 = 𝜎(𝐸 − 𝒖𝑩𝑧 )(1.49)The equation (1.46) and the equation (1.48) are assigned to the equation (1.47)
𝑚̇ 𝑑𝒖
1
𝑑𝑩𝑧
1
= − 𝑩𝑧 () = − 𝑑𝑑𝑥𝑩2𝑧
𝑑ℎ 𝑑𝑥
μ
𝑑𝑧
2μ

(1.50)The integral of the equation (1.46), (1.47), (1.50) from the propellant surface to the pointof magnetic sound velocity are described as𝜌∗ 𝒖∗ 𝑑ℎ = 𝑚̇
𝑚̇ ∗
1
𝒖 =
(𝑩2 − 𝑩∗2 )
𝑑ℎ
2μ 0
𝑚̇
𝐸𝑩0 𝑚̇
𝒖∗2
𝐸𝑩∗
ℎ0 +
=
(ℎ∗ +
)+
𝑑ℎ
μ
𝑑ℎ
2
μ

(1.51)(1.52)(1.53)

By above equations and the equation (1.43), the magnetic field at magnetic sound velocity
point is shown by
𝑩0(1.54)𝑩∗ =√3
Furthermore, by above equation and the equation (1.46) and (1.47), the magnetic soundvelocity can be given by16∆ℎ𝒖∗ = √√3 − 1.5(1.55)

where ∆ℎ equals ℎ∗ − ℎ0 . If a specific energy for ionization or other somethings isassumed that it equals the enthalpy change Δh of flow, the magnetic sound velocity u* isconstant and proportional to Alfven critical velocity ucrit which is given by𝒖crit = √2∆ℎ = √2𝑒𝑉𝑖
𝑀(1.56)

where M is a mass of propellant molecule accelerated by ucrit. By the equation (1.55) and(1.56),
𝒖∗ =

𝒖crit

1

√2 √√3 − 1.5= 1.47𝒖crit(1.57)As shown in equation (1.53), a difference in magnetic pressure from the propellant surface
to the point of magnetic sound velocity decides a mass flow ratio per aria unit if u* isconstant. In addition, by assignment equation (1.44) and (1.54) to equation (1.53), themass flow rate is depended on the square of current J and channel width. In other words,
the mass flow rate 𝑚 ≈ ̇ ∆𝑚 is proportional to the square of discharge current. Therefore,
PPT has a tendency as follows𝑚̇ ∝ 𝑭 ∝ 𝑱2

(1.58)The thrust by electromagnetic acceleration is described with same form of equation (1.53)
as
𝑚̇
1 2
𝑼𝑒 =
𝑩
𝑑ℎ
2μ 0

(1.59)

where Ue is an exhaust velocity. The thrust FEM by electromagnetic acceleration is
𝑭EM = 𝑚̇𝑼e1
= 𝑑ℎ 𝑩20
2μSince the magnetic flux density at propellant surface is expressed as B0=μJ/d,
17(1.60)

1 μ𝑱 2
𝑭EM = 𝑑ℎ ( )2μ 𝑑(1.61)

μ𝒋2 ℎ
2 𝑑(1.62)=

By the integration of above equation over time t, impulse bit Ibit is given by

𝑰𝑏𝑖𝑡 =

μℎ 𝑇 2∫ 𝑱 𝑑𝑡2𝑑 0(1.63)

1.6.3. The model applying electrothermal acceleration
Guman et al derived the thrust by electorthermal acceleration with assumption thatthe generated gas is expanded to vacuum when the energy E0 is supplied to the propellant
gas of volume V due to the discharge[5]. In addition, following conditions are applied
・Initial temperature is sufficiently lower than final one.
・Unsteady pressure wave propagates rapidly.
・Average flow velocity is sound velocity.
・Gas expansion is adiabatic.
・Cross section area is constant during flowing.
Therefore, the impulse bit by electrothermal acceleration can be given by128(𝛾 − 1)
𝑰bit,ET = [ 2∆𝑚𝑬0 ]𝛾 (𝛾 + 1)

where γ is a specific heat ratio.

18(2.62)

Chapter 2: Experimental equipment
In this chapter, experimental equipment and its principle will be explained. The
experimental system is constructed by several part such as APPT power source, ignitercontrol device, vacuum exhaust system, thrust measuring system. Since PPT generates
momentum force (unsteady force), PPT is generally evaluated with impulse bit. Therefore,
the basic evaluation is carried out with impulse bit and its consumed energy andpropellant mass.

2.1. Experiment system
The operating system is shown in Figure 2.1. The order from PPT operation tomeasurement various parameters are in the following:
1. Capacitor for main discharge is charged from 500 to 1000 V by VC power source.
2. Start measurement by impulse bit measurement device and set the current andvoltage measurements to the trigger standby state.
3. The signal generator sends a 60 Hz pulse signal to the igniter module in responseto an instruction from PC.
4. PPT operates and releases plasma by small discharge of igniter.
5. The oscilloscope records the discharge current and voltage waveform from
Rogowski coil and high voltage measurement probe triggered by itself.
6. The exhaust gas collector of the impulse bit measurement device receives theexhaust gas from the PPT, and the impulse bit data is output as displacement
value measured by the laser displacement detector.
7. Wait until the oscillation of the impulse bit measuring instrument has settled andmeasurement is available again.
8. Repeat from 1 to 7
The thrust of PPT must be measured several times at once because solid propellant
ablation is not always the same at each work. In other words, the impulse bit
measurement must be performed statistically. Furthermore, the state of solid
propellant surface will be changed, so thrust must be measured once every several
hundred times operation. The capacitor is charged at 100 mA and is completed inapproximately 10 seconds at the maximum. Therefore, the pulse signal is set to transmit
according to the charging time, and PPT can be operated automatically. At sometimes,
PPT may not work due to igniter malfunction or small plasma production failure even if
a signal is sent. Since current and voltage are no change when PPT does not operate, the19Control and measurement system
PC

Oscilloscope
Displacement
PC based measurement

signalCapacitorand signal generation

voltage

Discharge
current

Thrust measurement device
PlasmaPPT
Rogowski coil
Vacuum chamber

Turbo molecular
Ionization

Igniter module

pumpPower supply forgauge

main discharge

Igniter power(Max 1kV)

source (Max6 kV)

Rotary pump

PPT power supply system
Vacuum system
Figure 2.1. Schematic of entire experimental systemoscilloscope is set to save the data when the current trigger is detected, and the numberof operations is counted by the number of recorded data.

2.2. Measurement and control equipment
The discharge period is expected that it is extremely short from approximately several
tens microseconds to few microseconds. Therefore, the current and voltage waveform
measurement equipment is required high resolution. On the other hand, due to the20principle of thrust measurement equipment, the measurement is for several seconds order.
Since measurement period of waveform and thrust are much difference, these systems isrequired to divide.
PPT control is simple because there is only igniter control. That is, it is enough toprepare only the signal generator.

2.2.1. Impulse bit signal receiver and igniter signal
generator
The PC-based measurement instrument (WE 500) is adopted to receive thrust datafrom the thrust measurement device and to transmit s igniter signal. This instrument cantransmit or receive various signals by exchanging modules. However, since it is notinstalled some interface such as monitor, it is necessary to connect to a PC for waveform
monitoring and signal transmission.
The signal for igniter is set 60 Hz pulse waveform, as its detail will be explained later,
this frequency is decided due to the igniter power source is 60 Hz alternating current. The
reason of pulse waveform is that the signal receiver of igniter module is relay circuit, so
control with a digital signal is preferable. Duty ratio is 50 %. This signal is transmitted toigniter module between 0.1 Hz and 1 Hz depend on PPT settings.
The thrust information is output as voltage in the range -10 to 10 from thrustmeasurement device. The output data draws a damped oscillation waveform from 1 to 0.8
Hz. After about 10 seconds from the PPT operation, the damping is completed and thenext thrust measurement is standby state.
By the similar frequency of signal transmitting and data receiving, these can be
performed on the same device.

2.2.2. Rogowski coil
The maximum discharge current is estimated approximately 21 kA if it is assumed
that current is constant and discharge period is 5 µs. As a method of measuring such ahigh current waveform, small resistance at 10-3 Ω is often inserted into the target circuit.
However, inserting resistance causes to decrease PPT performance due to increaseinductance or resistance in discharge circuit. That is, this method cannot be hired to thisexperiment.
In this research, Rogowski coil is applied to measure current because this instrument
has some advantages for this experiment as follows: Almost no influence on the target circuit due to the non-contact measurement.
21

It is high frequency responsiveness characteristics and can correspond to currents
with high peak values.
 Easy to downsize and measurable even small circuit such as PPT discharge
circuit.
 By the system separated from the circuit including other measuring instruments,
noise and ground interference can be avoided.
As shown in Figure 2.2, Rogowski coil is shaped in which a solenoid coil is wound
up, and the target current flows its inside.

Figure 2.2. Rogowski coil principle [14]Here, Any closed curve S surrounding current density vector i is considered. Magnetic fluxΦ interlinking solenoid is given by𝛷 = ∮ 𝑛𝑎𝜇𝐻𝑑𝑆 + ∫ 𝐵0 𝑑𝐴
𝑆

(3.1)

𝐴

where n is number of turns per unit length of solenoid, a is cross section area of solenoid,
μ is permeability, H is magnetic field vector by current i, B0 is magnetic flux density
which is interlinked closed curve area by S, A is area vector formed by closed curve S.
As shown in Figure 2.2, if rogowski coil is made as rewinding shape, in other words, if
one terminal of the coil is made so as to penetrate the cross section area a, the second
term in above equation is canceled and becomes 0. Therefore, equation (3.1) becomes22

(3.2)

𝛷 = ∮ 𝑛𝑎𝜇𝐻𝑑𝑆
𝑆

By Ampere’s law(3.3)∮ 𝑖 = ∮ 𝐻𝑑𝑆
𝑆𝑆Therefore,𝛷 = ∮ 𝑛𝑎𝜇𝐻𝑑𝑆 = 𝑛𝑎𝜇 ∮ 𝑖𝑑𝐴
𝑆

(3.4)

𝑆

Faraday's law is given by𝜏𝛷 = ∫ 𝑒𝑅 (𝑡)𝑑𝑡

(3.5)

0

where τ is integration time, eR(t) is electromotive force between electrodes. If the entire
target current is defined as 𝐼 = ∮𝑆 𝑖 , the output from Rogowski coil is described as

𝐼=
=

1
𝛷
𝑛𝑎𝜇
𝜏
1
∫ 𝑒𝑅 (𝑡)𝑑𝑡
𝑛𝑎𝜇 0

(3.6)

As equation (3.6), the current through into Rogowski coil can be calculated by integrationof output voltage. There is a method using integration circuit constructed with resistanceand capacitor, however, in this research, current waveform is obtained by analytically.
The Rogowski coil used in this research is made by us as shown in Figure 2.3. In thecalibration, this coil is connected to oscilloscope via BMC cable. It is calibrated with 15
kHz alternating current at 20 A, and its sampling interval is 1.0×10-7 s. Figure 2.4 shows
values that the obtained data just be integrated and multiplied by 1/naµ. Peak values areshown in Tabale 2.1. The average of peak current is 13.3 A and the standard deviation is
4.75×10-1 A. If original current peak value is assumed at 20 A, the calibration coefficientis 1.509.

23

Figure 2.3. Rogowski coil appearance

Current[A]

10

0

-10
0

0.00050.001

Time[t]Figure 2.4. Calibration current from Rogowski coil

Table 2.1. Current Peak Values at calibration

Sample number

Current peak value[A]

1
2
3
4
5

12.7
12.7
13.2
13.2
12.7
24

6
7
8
9
10

13.1
13.4
13.7
13.8
14.1

Average

13.3

To confirm this calibration coefficient, Table 2.2 shows analyzed current values andits error by multiplication values in Table 2.1 by obtained coefficient. Here, the standard
deviation of current peak is 0.72 A and the absolute value average of error is 0.59 A.
Since the order of current value of our PPT is estimated as several ten kA, and standard
deviation and error average are less than 0.1 % of this order, this Rogowski coil including
measuring devices is sufficiently acceptable for current measurement of our PPT.
Table 2.2. Analyzed Current Peak Values and its errors at calibration

Sample number

Current peak value[A]Error[A]

1
2
3
4

19.12
19.2
19.94
19.91

0.88
0.8
0.06
0.09

5
6
7
8
9
10

19.12
19.76
20.18
20.65
20.79
21.34

0.88
0.24
-0.18
-0.65
-0.79
-1.34

Average20

7.1054E-16

Other characteristics of this Rogowski coil are summarized in Table 2.3.
Table 2.3. Characteristics of Rogowski coil

Total turns number N
Inside diameter
Solenoid diameter
Solenoid length
Turns number per unit length n
Cross section area a25

50
13.0 mm
7.5 mm64.4 mm
573.9 mm-1
44.2 mm2

3.14×107 A2/Nm2
0.93

1/naµ
Calibration factor

2.2.3. Discharge current and voltage waveform
measurement
Discharge period of PPT is approximately several ten microseconds, naturally, ameasurement instrument must correspond to this order. Furthermore, the current from
Rogowski coil is extremely large, naturally, measurement instrument will be broken if it
is connected directly. Therefore, for this measurement, digital phosphor oscilloscope(DPO 4104B-L) produced by Tektronix Co. Ltd is hired, its maximum measurement
frequency is 1 GHz. In addition, Rogowski coil is connected via attenuator at -30 dB with
1 W (made by Stack Electronics Co,Ltd.). If the signals is sent via attenuator, the relation
between original and detected signal is given by
𝑉𝑖 2
𝐺𝑝 = 10log10 ( )
𝑉𝑜

(3.7)

where Gp is attenuation amount, Vi is attenuated signal, Vo is original signal. Since Gpequals 30 dB,

𝑉𝑜 = √𝑉𝑖2 × 103(3.8)

The obtained signal must be converted with above equation.

2.3. Power supply
The PPT in this research is assumed that charge voltage is from 500 V to 1 kV. In
addition, to operate igniter in vacuum requires momentarily high voltage at approximately
several kV.

2.3.1. Power supply for PPTElectric power supply capacity is related with frequency of PPT operation. If a lot of
operation is planned, better performance power supply unit should be prepared to avoid
experiment period being redundant.

26

Two power supply unit is prepared in this experiment. One of them is that maximum
supply voltage is 500 V and current is 600 mA. Another one is that maximum supply
voltage is 1 kV and current is 50 mA. The former will be used in lower voltage experimentat less than 500 V, and the latter will be used higher voltage experiment.

2.3.2. Igniter module
In this experiment case, igniter module including booster circuit is not put into
vacuum chamber. Therefore, it must boost in outside and supply to igniter electrodedirectly in vacuum. Discharge in vacuum is required higher voltage than underatmosphere. Relation of gap d between two electrodes, pressure p between electrodes andstart point voltage Vs of discharge is described by Paschen’s law as
𝑝𝑑

𝑉𝑠 =
ln [
=𝐵

(3.9)

𝐴𝑝𝑑
1

ln(1+𝛾)]𝑝𝑑
𝐶 + ln(𝑝𝑑)(3.10)

where γ is average of emitted secondary electrons from cathode surface due to the impact
by one positive ion, A and B are decided by relational expression given by𝐵
𝛼 = 𝑝𝐴exp [− 𝐸 ](3.11)

𝑝where α is impact ionization coefficient, E is electric field. By the equation (3.10), Vs isconvex function which include one minimum value. Term of pd should be extremely
small value, because pressure p is expressed vacuum pressure as space, which is 10-5 torr
class. In the actual case, Paschen’s law cannot be established at less than that pressure.
Therefore, estimated discharge start value by above expressions is just a guide, so exact
value is needed to find by experimentally. According to past experiment, the record ofdischarge at 3 kV was reported. That is, igniter module is made that can generate from 3
kV to 6 kV.
The schematic of igniter module circuit is shown in Figure 2.5. The output voltage
can be adjusted by variable autotransformer from 0 V to 100 V. Its operation is controlled
by switching relay circuit. The output voltage from variable autotransformer is boosted
by voltage converter that convert ratio is 1:60. Therefore, this module can supply from 0
kV to 6 kV.

27

Signal from PC
Transformer

Output to igniter

Relay circuit

Variabletransformer
AC 200 V
Output to igniter

2.4.

Figure 2.5. Schematic of igniter module

Thrust measuring system
The possible thrust of PPT is extremely feeble and momentary. Thus, the special
measurement equipment which called “Thruster Stand” exists for electric propulsion unit.

2.4.1 Thruster standThruster stand is usually pendulum construction measurement equipment including
spring-mass-damper system. Since thrust is amplified by pendulum construction, tiny
power measurement is enabled. If a propulsion unit is independent, it can be measured
directly with mounting condition on this equipment. However, the PPT of this experimentcannot be applied this method because it must be connected to outside devices of thesystem and a cable tension or mass interfere to detected value. For this reason, thisMagnet damper

Leaf spring axis

TargetExhaustLaser displacement detector

PPT

Figure 2.6. Thruster stand principle
28

experiment is hired measurement method that thrust is measured by receiving exhaustfrom PPT.
As shown in Figure 2.6, this equipment is constructed of 4 part which is exhaustcollector (called target), leaf spring axis, magnetic damper and laser displacement
detector. When PPT is operated, particles such as plasma or neutral gas is ejected andimpact target. Then, thruster stand begins swinging periodically with the maximum
displacement at the balance point with reaction force of leaf spring. Oscillation is damped
by magnetic damper, and its waveform is monitored by laser displacement detector. PPT
thrust is evaluated by impulse bit, and it is proportional to maximum amplitude of thiswaveform [15][16]. Therefore, the maximum displacement is recorded.
The target is a cylindrical shape with a lot of slit on the side, and its bottom is aconical shape. The reason of this shape is to prevent error caused by reflected particle
between target and PPT by changing direction particles motion in the radial direction.
This target is made of 3D-printed high heat resistance resin.

2.4.2 Calibration
The performance of PPT is generally evaluated with impulse bit due to the pulse
operation. Therefore, in this experiment, impulse bit by PPT should be converted andobtained directly from displacement data, and calibration coefficient must be able toconvert these two elements. As shown in Figure 2.7, calibration is carried out by hummer
hitting the target side shaft of thruster stand actually and giving impact. The force of this
impact is measured by force transducer which is attached on the tip of hummer. The
hummer is pendulum shape as shown in Figure 2.8, and it is pulled and swung by humanhand. The impulse bit of hummer impact is calculated by integration of measured force
by sample interval time. The waveform of obtained displacement data describes damped
oscillation because thruster stand is damped oscillation system including mass, spring anddamper. Since the maximum amplitude of this oscillation and calculated impulse bit byhummer are proportional, thruster stand is calibrated by taking these two values multiple
times and comparing them. The relational expression of impulse bit I and maximum
amplitude Amax is given by𝐼=

𝑙𝑐𝑎𝑙 𝐼𝑓𝐴
𝑙𝑡 𝐴𝑐𝑎𝑙 𝑚𝑎𝑥

29(3.12)

Hummer with force transducer
Magnet damper

Leaf spring axis

ImpactSwing

TargetExhaustLaser displacement detector

PPT
Figure 2.7. Thruster stand calibration method

where lcal is the length of force transducer impact point from leaf spring axis, lt is thelength of target from leaf spring axis, If is impulse bit by the calibrator, Acal is maximum
amplitude by the calibrator. Here, If /Acal is given by least-square method∑𝑖 𝐴𝑐𝑎𝑙,𝑖 𝐼𝑐𝑎𝑙,𝑖𝐼𝑓=∑𝑖 𝐴2𝑐𝑎𝑙,𝑖𝐴𝑐𝑎𝑙(3.13)

Calibration is performed before and after each measurement because target massprobably be changed by contamination of ejected propellant. The force transducer is LVS500GA made by Kyowa Electronic Instruments Co., Ltd. Its measurable maximum force
is 5 N and its error is plus or minus 0.5 %. Therefore, it is guaranteed up to 0.05 N order.
If discharge time is assumed to be 10 µs, measurable impulse bit order is 0.5 µNs and it
can satisfy the requirement of measurement for PPT impulse bit. One of the example data

Figure 2.8. Pendulum type Calibration hummer
30

Force transducer signal [V]is shown in Figure 2.7 and 2.8. For Figure 2.7, the force transducer signal describes theoscillation waveform. Since it is considered that the tip of the force transducer vibrates
after the collision, the first peak of this waveform should actually be analyzed as impulse.
The correlation of this calibration is shown in Figure 2.9. Since there is high correlation
which R-square value is 0.9941, the linearity of the output of the thruster stand and theimpulse bit should not be a problem.

3
2
1
0
-1
-0.002

0

0.002

0.004

Time [s]Laser displacement signal [V]Figure 2.9. Example of calibration data of force
transducer

1
0.5
0
-0.5

Maximum-1

displacement point

0

5

10

15

20

Time [s]Calibrator impulse [N・S]

0.008

Figure 2.10. Example of calibration data of thruster stand0.006|r|=9.941e-01

0.004
0.002
0
0

0.001

0.002

0.003

Thruster stand displacement [mm]Figure 2.11. Example of calibration line
31

0.004

2.5. Vacuum system
As shown in schematic in Figure 2.10, vacuum system is consisted of a vacuum
chamber, a rotary pump, a turbo molecular pump, valves and vacuum gages (Pirani
gauge, ionization vacuum gauge). This vacuum chamber is evacuated by a rotary pump
and a turbo molecular pump connected in series. The vacuum chamber is installed roundand rectangular windows on the side and one round window on the back side. The
appearance of vacuum chamber is shown in Figure 2.11. The minimum vacuum pressureis 1.0×10-5 torr. Pirani gauge is used in the range of 0.1 to 760 torr, and ionization
vacuum gauge is used at less than 10.0×10-3. Experiment is performed at 1.0×10-5 to
5.0×10-5 which is a high vacuum zone.

32

Leak valve

Ionization vacuum
gauge

Vacuum chamber

Pirani gaugeTurbomolecular

pump

Valve 1

Valve 2

Rotary pump

Oil Mist Trap
Figure 2.12. Schematic of vacuum system
33

Figure 2.13. Appearance of vacuum chamber

2.6. High speed camera (FASTCAM SA-Z)
To observe plasma behavior, high speed camera (FASTCAM SA-Z: PHOTRON
LIMITED Co., Ltd., Figure 2.12) is installed at vacuum chamber aside. Shooting
conditions are that the resolution is 120×74 pixels and shooting speed is 504000 fps.

©PHOTRON LIMITED Co., Ltd.

Figure 2.14 FASTCAM SA-Z: PHOTRON LIMITED Co., Ltd.
34

Chapter 3: Perforated Solid Propellant
Verification
Originally, a propulsion unit for an artificial satellite generally mounts propellant
without any gaps in order to effectively use its small mounting space. Therefore, it isnatural that the solid propellant for PPT is a simple shape such as rectangularparallelepiped or cylinder. However, since the performance changes depending on the
shape of the PPT, the possibility that the performance changes depending on the solid
fuel shape of the PPT is also estimated. In this experiment, a new approach to the PPT
performance production was carried out.
In this experiment, the thrust and consumed mass are measured and compared withnormal solid propellant and perforated solid propellant. Both propellants are respectively
tested with two different charging voltages at 500 V, 750 V and 1000 V.

3.1. Laboratory PPT
The appearance of experimental PPT for this work is shown in Figure3.1. This unit
is a breech-fed electromagnetic acceleration type PPT with rectangular parallel electrodes.
Since PPT is put into vacuum, film capacitor is installed. As shown in circuit diagram(Figure3.2) the capacitor capacity C is 420 µF. Its rated voltage is 1100 V. The gap
between electrodes is 15 mm and its width is 10 mm, and its thickness is 2 mm. In addition,
this PPT is hired flaring tongue shape electrode, which is reported that yielded an increasein thrust efficiency by nearly 35 % and in exhaust velocity of nearly 20 % [19][20]. The
length of this discharge chamber is 20 mm up to the bent part and 20 mm where flaring
part. The angle of flaring is 30 degrees. In order to prevent the influence of contamination,
electrodes are polished after every experiment to remove the attached carbon. The igniteris biaxial and hired a combination of tungsten and tritungsten at the discharge terminal
part, and the thickness is 0.5 mm for tungsten and 0.1 mm for tritungsten. The distance35

between igniter tips is approximately 0.5 mm. Installing position is 1 mm from the solid
propellant. The solid propellant material is PTFE.

Figure 3.1. Laboratory PPT for perforated solid propellant

PPT anode

2.5 kΩ

Power supply

100 MΩ
420 µF

500 – 1000 V

PPT cathodeFigure 3.2. PPT circuit diagram

3.2. Normal shape solid propellant test
3.2.1 Normal shape PTFE solid propellant experiment
A large number of propellant types have been evaluated in the hopes of finding
improvements over PTFE. The evaluations are usually performed by measuring thrust
performance, and by examining the posttest condition of the ablated surface. For example,
36

the other propellants showed variations in Isp from 947 s (Kel-F) to 2410 s (polyethylene)
with PTFE at 1085 s in a breech-fed configuration [21]. As in this example, there aresome higher efficient as solid propellant which does not include contamination materials
such as fluorine. Nevertheless, the reason why PTFE is selected as PPT solid propellant
is its stability for heat. From the previous example, the melting point of polyethylene isfrom 120 to 140 degree, however, PTFE is 327 degrees. This characteristic is effective toprevent LTA. In addition, it is also an advantage that the stability of the propellant ismaintained during continuous operation. Due to those reasons, PTFE was applied as solid
propellant in this experiment.
As shown in the Figure3.3, the consumption surface shape of normal shape solid
propellant is 15 mm in height and 10 mm in width. The area of consumption surface is
150 mm2. After the propellant bar is cleaned by an ultrasonic cleaner, its mass is measured
by electronic analytical scale. After experiment, propellant bar is removed and measuredhw

Figure 3.3. Normal shape PTFE solid propellant, h = 15 mm, w = 10 mmdirectly its mass again. The consumed mass is evaluated by dividing the measured
consumed mass by the number of operations.
Figure 3.4 and 3.5 shows the preparation state of the experiment. PPT is fixed with
its tip inserted approximately 30 mm into the thruster stand target that is stationary state.
Usually, after the solid propellant is sublimated and ionized, it is formed a current sheet
due to a pinch effect by electric current, and is ejected by Lorentz force. However, a partof plasma is ejected without a Lorentz force from the side of the discharge chamber due
to volume expansion when be sublimated. Since these particles contribute to thrust eventhough they are minute, they must be collected by the target as much as possible. In
37

addition, the same applies to neutral gas which is generated due to the LTA after theplasma is exhausted. The Rogowski coil is attached to the cathode (upper side) as
Figure3.4. The current in the cathode is measured by it. The Rogowski coil surface iselaborately insulated to prevent discharge through the coil. The voltage is measured
between capacitor terminals by high voltage probe.

Figure 3.4 Experimental set up appearance from back side

Figure 3.5 Experimental set up appearance from vacuum chamber side window

38

3.2.2 Result and discussion
Normal PTFE solid propellant was installed, and experiment was carried out withseveral hundred operations. Figure3.6 shows the appearance of PPT during discharge.
Each number of operation is 902 times at 500 V charge, 1000 times at 750 V charge and607 times at 1000 V charge. These difference in operation numbers is caused due to

Figure 3.6 PPT appearance during discharge

igniter malfunction. Probably, there are three reasons of this matter, first one iscontamination between igniter terminals by the adhesion of carbon which is one of thePTFE component, second one is that supply voltage to igniter was low for experimentvacuum level, and last one is increasing electric resistance due to the Joule heating. For
the first reason, igniter tip point, especially inserted part into discharge chamber, wascontaminated black stain after experiment. As considering PTFE components, this stain
is obviously carbon. This contamination causes discharge difficulty due to electric
resistance increasing between terminals or terminals conduction at worst case. This mattermight be improved by applying single terminal igniter. This type igniter is mounted only
positive terminal on the cathode of discharge chamber and negative side of igniter isconnected to its cathode. Since a spark is occurred between the igniter terminal anddischarge chamber cathode, a dischargeable area of igniter spark is enlarged and theaffection of contamination to igniter is reduced. However, this constitution has apossibility that affection to measure a discharge current by Rogowski coil. Therefore,
biaxial terminal igniter is appropriate for this measurement because its circuit isestablished as one module. The second reason was suggested due to that when the PPT
did not work, a little flash at tip of igniter was also not observed in any malfunctions eventhough operation number was few. The dischargeable voltage in vacuum is extremely
higher than the voltage in atmospheric pressure at room. If a voltage of igniter issufficiently, the flash should be observed between igniter terminals. In this research, we39were not able to prepare a higher voltage supplier, therefore, if we will continue this typeresearch in the future, we must create circuit which can generate ten kV order discharge
voltage controlled by NOSFET including capacitor and transformer. For the last reason,
we did not measure a temperature of igniter, however, it is presumed by a fact that almost
igniter malfunction occurs suddenly after several times continuous operation. Since a
contact area of igniter for any other parts is small, the igniter can lower itself temperatureby only radiation. Furthermore, even if current value of one operation is small, theoperation is performed a plurality of times continuously, so that the next operation is
performed before the heat dissipation is completed. In other words, Joule hearting of one
operation is small, however, temperature increase due to the continuous operation. To
improve this matter, a terminals exposed area must be enlarged to increase an amount ofheat dissipation by radiation from igniter surface.
The measured impulse bits are shown in Figure 3.7, 3.8 and 3.9. In addition,
theoretical impulse bit calculated by measured current are also described in each figure.
Impulse bit was measured five times in a row at several operation numbers that are fromfirst operation, from 100 times operation, from 500 times operation. The 750 V chargecase was performed after other cases experiment and be measured from first, 500 times
and 1000 times operation. The average of measured impulse bit and calculated theoretical
impulse bit in each charge voltage are shown in Table 3.1. For Figure 3.7 and 3.8, ineither case, the impulse bit decreases as the number of operation increases.

Impulse bit [Ns][10-2] 1
Measured
Theoritical

0.8
0.6
0.4
0.2
0

0

100

200

300

400

500

Operation number [-]Figure 3.7. Comparison of measured impulse bit and theoretical impulse bit calculated bycurrent data in normal shape solid propellant at 1000 V40[10-3] 5
Impulse bit [Ns]43
Measured
Theoritical

2
1
0

0

200

400

600

800

1000

Operation number [-]Figure 3.8. Comparison of measured impulse bit and theoretical impulse bit calculated
by current data in normal shape solid propellant at 750 V

Impulse bit [Ns][10-3] 1.5
Measured
Theoritical
1

0.5

0

0

100

200

300

400

500

Operation number [-]Figure 3.9. Comparison of measured impulse bit and theoretical impulse bit calculated
by current data in normal shape solid propellant at 500 V

As canbe seen from the Figure 3.9, the surface of the electrode was contaminated with carbon.
Table 3.1. Average values of measured impulse bit and calculated theoretical
impulse bit and its ratio
Supply voltage [V]
1000
750
500
Impulse bit average [µNs]

2174

1109

411

Theoretical impulse bit average [µNs]

6535

4263

831

Ratio of measured value and theoretical one [%]

33.3

26

49.5

41

Figure 3.10. Anode (upper) and cathode (lower) appearance with contamination of carbon after
experiment of normal shape solid propellant

Contamination is more terrible on the cathode (lower electrode in figure). In contrast,
anode is contaminated at only the vicinity solid propellant without center. Figure 3.11
shows the maximum current transition. For this graph, the current value decreases as thenumber of operation times increases. This transition also suggests possibility that theelectric resistance value in the discharge circuit is increased. In addition, by the equation(1.63), it is proved that this PPT accelerates and ejects the plasma by the Lorentz force
because the measured impulse bit is proportionally supply voltage. The theoretical
impulse bit can be calculated with measured current data by equation (1.16), and be also
shown in each figure. Tendencies of theoretical impulse bit for operation number are also
decreasing in 1000 V and 750 V cases. However, its rate of variation is not similar withmeasured impulse bit. In only 500 V charge case, it is increased and is also not similar
with measured value. In addition, theoretical values are larger from 2 to 5 times than
measured value. This fact indicates one possibility that almost electric energy charged incapacitor was wasted as heat energy. An electromagnetic acceleration amount for one
particle is limited due to the receivable energy limitation. If supply energy exceeds thislimitation, this particle causes further ionization or excitation and absolutes supply energy
as internal energy. In other words, almost excessively supply energy for unit mass of42

[10 ]

3

Maximum current [A]propellant is converted to heat energy and cannot contribute to kinetic energy.

2.8

4

2.6
2.4
2.2
2

0

100

200
300
400
Operation number [-]500

Figure 3.11 Maximum current of normal shape solid propellant at 1000 V

Figure 3.12 shows that the movement of plasma in 2 µs at 16 µs after beginningplasma generation. It appears that the current sheet was formed between electrodes and it
moves to downstream along electrodes.
Solid propellant

Igniter

Electrodes
Electrodes

Figure 3.12. Plasma movement for 2 µs taken with a high-speed camera at 500 V in normal shapesolid propellant

Measured consumed mass is shown in Table 3.2 with operation number. The second
row of this table shows total consumed mass before and after experiment, and the third
row shows that the second row value is divided by operation number in the first row. Dueto the different operation number, the total consumed mass with 500 V charge is higher
than 1000 V charge by approximately 65 %. For this fact, it can be seen that the massconsumption at one operation increases as the input power increases in normal shape case.
In addition, Table 3.2 also show the calculated momentum coupling coefficient with43

related values. The voltage values explained so far are only target values and may differ
from the actual values depending on the performance of the power supply unit. Therefore,
the voltage value used for such calculation is applied an actual value measured by a highvoltage probe. The amount of charged energy in capacitor of the second row is calculatedby the input voltage. This momentum coupling coefficient was calculated with this energy
and the average of impulse bit. As can be seen from this value, the coefficient of 1000 V
charge is highest than others. As a result, the propulsion efficiency increases as the supply
energy increase.
Table 3.2. Summary of measured parameters of normal shape solid propellant
1000V
750V
500V
Operation number

607

1031

902

Consumed mass [g]

0.033

0.04

0.03

Consumed mass per operation number [g]55.1×10-6

39.3×10-6

33.4×10-6

Actual measured average voltage [V]

976

744

470

Input energy [J]

200

116.2

46.4

Momentum coupling coefficient [Ns/J]

10.9 ×10-6

9.72×10-6

8.85×10-6

3.3. Perforated solid propellant test
3.3.1 Perforated solid propellant
Figure 3.13 shows perforated solid propellant. Its material is PTFE, and its height,
width and depth sizes are the same as for normal solid propellant. There are 5 holes in theheight direction at 2 mm intervals, and these holes are 3 rows in the width direction at 2.5
mm intervals. A total of 15 holes are evenly drilled. The hole diameter is 1 mm and its
depth is approximately 20 mm. The area of consumption surface is 138.2 mm2, which isequivalent to 92.00% of normal shape solid propellant. Therefore, impulse bit will bedecreased 8.00 % than normal propellant case. However, consumed mass will bedecreased 6.67 % than normal one due to the ratio of propellant surface area which isirradiated radiation.
The procedure of the experiment is the same as that of normal shape. Impulse bit andconsumption mass are measured at 500V charge and 1000V charge, respectively. One
difference from normal shape case is the processing after cleaning the propellant. Alcohol
is used for cleaning with an ultrasonic cleaner before the experiment, however, it may
enter into propellant holes and cause an error in mass measurement. Therefore, in thenormal shape experiment, the perforated solid propellant after cleaning is left in thevacuum chamber to evaporate and completely remove the attached alcohol. Then, its massis measured and the experiment is carried out.
44

Figure 3.13 Perforated solid propellant

3.3.2 Perforated solid propellant result and discussion
Perforated solid propellant test was also carried out with same supply voltage andcondition. Each number of operation is 394 times at 500 V charge, 1000 times at 750 V
charge and 607 times at 1000 V charge. The reason of 500 V charge case operation
number is less than 500 is igniter malfunction same as normal shape test. However,operation numbers of 1000 V and 750 V charge is purposely adjusted to the operation
number of normal shape case.
The each measured impulse bit is shown in Figure 3.14, 3.15 and 3.16. Impulse bit
was measured at the same operation number as normal shape experiment.

45

Impulse bit [Ns][10-2] 1
0.8
0.6

Measured
Theoritical

0.4
0.2
0

0

100

200

300

400

500

Operation number [-]Figure 3.14. Comparison of measured impulse bit and theoretical impulse bit calculated bycurrent data in case of perforated solid propellant at 1000 V

Impulse bit [Ns][10-3] 5
4
3

Measured
Theoritical

2
1
0

0

200

400

600

800

1000

Operation number [-]Figure 3.15. Comparison of measured impulse bit and theoretical impulse bit calculated
by current data in case of perforated solid propellant at 750 V

46

Impulse bit [Ns][10-4] 5
4
3
2
1
0

0

50

100

Operation number [-]Figure 3.16. Impulse bit of perforated solid propellant at 500 V

However, measurements from 500 times of 500 V charge were not performed due to themalfunction of igniter. Therefore, two impulse bit data from 45 times that was acquired
for reference is shown alternatively. The 750 V charge case was performed after othercases experiment and be measured from first, 500 times and 1000 times operation. In
addition, theoretical impulse bit is calculated by measured current value and describedeach graph. However, theoretical value of 500 V charge case was not calculated because
it was confirmed that Rogowski coil was removed from PPT electrode after experiment.
Therefore, this value is not described. The average of measured impulse bit and calculated
theoretical impulse bit in each charge voltage are shown in Table 3.3. In the case of 1000
V
Table 3.3. Average values of measured impulse bit and calculated theoretical
impulse bit and its ratio
Supply voltage [V]
1000
750
500
Impulse bit average [µNs]

1910

1005

414

Theoretical impulse bit average [µNs]

8681

3853

-

Ratio of measured value and theoretical one [%]

22

26.1

-

charge, measured and theoretical impulse bit decrease as the number of operations
increases such as normal shape solid propellant results. In the other hand, these values of
750 V case reduced once and increase and become similar value with initial one.

47

Furthermore, the impulse bit with 500 V charge increases as the operation number
increase.
Figure 3.17 shows that the movement of plasma in 2 µs at 16 µs after beginningplasma generation. It appears that the current sheet was formed between electrodes and it
moves to downstream along electrodes.
Solid propellant

Igniter

Electrodes
Electrodes

Figure 3.17. Plasma movement for 2 µs taken with a high-speed
camera at 500 V in perforated solid propellant

The each consumed mass is shown in Table 3.2 with operation number. This result
is also similar to the normal shape solid propellant result, the consumed mass per one
operation at 1000 V charge is higher than 500 V charge, and this difference is 158 %.
Furthermore, Table 3.4 also show the calculated momentum coupling coefficient.
This value at 1000 V charge is highest. As a different from normal propellant case,momentum coupling coefficient of 750 V case is lowest.
Table 3.4. Summary of measured parameters of perforated solid propellant
1000V
750V
500V
Operation number

607

Consumed mass [g]

0.04

1000

394

0.05
-6

0.01
-6

25.7×10-6

Consumed mass per operation number [g]66.4×1049.3×10

Actual measured average voltage [V]

968

702

466

Input energy [J]

196.8

103.3

45.6

Momentum coupling coefficient [Ns/J]

9.80×10-6

7.65×10-6

9.08×10-6

For the above results, in the perforated solid propellant case, the relation of supplied
power and each parameter such as impulse bit, consumed mass, momentum coupling
coefficient is similar with normal shape solid propellant. Furthermore, in the case of
1000V charge, the transition of impulse bit and maximum current versus operation
48

number also correspond to normal one. In the other hand, in the case of 500 V charge, thetransition of impulse bit showed the opposite inclination.

3.3.3 Summary and comparison of perforated andnormal shape solid propellant
Up to the previous section, we have examined what kind of tendency is observed in
the case of each solid propellant. In this section, the perforated solid propellant results
obtained in the previous experiment is compared with normal propellant.
Measured impulse bits are summarized in Figure 3.18. In the 1000V charge case, theoverall impulse bit of normal solid propellant higher than perforated one, and which
average difference is approximately 12.5 %. Both transitions of impulse bits are very
similar in decrease tendency, however, slightly perforated solid propellant is more
gradual. In normally, the impulse bit generated by pulsed plasma thruster exponentiallydecreasing and asymptotically constant. Therefore, this phenomenon will be gently
converged. However, if this tendency continues, both impulse bit will be reverse at
approximately 2000 times operation. The operation number of PPT usually reaches overtens of thousands in one mission. Thus, perforated solid propellant may be advantageous
in over a long period mission because of stability of impulse bit. For 750 V charge case,
impulse bits show the opposite tendency each other, however, these values are similar
and its difference is 10.3 %. On the other hand, in the 500 V charge case, the impulse bitof normal shape solid propellant is 5.4 % higher than perforated solid propellant in initialpart of measurement, however, the impulse bit of perforated solid propellant increases.

49

The impulse bit of perforated propellant reached in the 100 operation times.

Impulse bit [Ns][10-3]

Normal at 1000 V
Normal at 750 V
Normal at 500 V
Perforated at 1000 V
Perforated at 750 V
Perforated at 500 V

2

1

0

0

200

400

600

800

1000

Operation number
Figure 3.18. Summarized all of measured impulse bit

All of calculated theoretical impulse bit are summarized in Figure 3.19. In contrast
to the measured values, perforated propellant with 1000 V charge case is highest. On theother hand, the difference of 750 V case is 10.6 %, and this percentage is similar withmeasured value. Since theoretical impulse bits are calculated by measured current value,
these facts indicate that an amount of total current of perforated propellant is supplied
excessively.

Impulse bit [Ns][10-2] 1

Normal at 1000 V
Normal at 750 V
Normal at 500 V
Perforated at 1000 V
Perforated at 750 V

0.8
0.6
0.4
0.2
0

0

200

400

600

800

1000

Operation number
Figure 3.19. Summarized all of calculated theoretical impulse bit transition

50

Figure 3.20 shows momentum coupling coefficient of each condition. For thesevalues, performances of all supply voltage and shape can be compared. Transitions of thecoefficient in the case of normal shape solid propellant at all voltages and perforated one
at 1000 V decreased. In contrast, the transition of perforated solid propellant of 500 V
case and normal propellant of 750 V case increased. In the case of perforated solid
propellant at 750 V charge, it decreased once and increased finally. The highest value isnormal shape solid propellant with 1000 V charge, however, assuming that the tendencyof perforated propellant with 500 V charge does not change, it will exceed at
approximately 180 operation times.

Momentum coupling coefficient [Ns/J][10-5] 1.2
Normal at 1000 V
Normal at 750 V
Normal at 500 V
Perforated at 1000 V
Perforated at 750 V
Perforated at 500 V

1.1

1

0.9

0.8
0

200

400

600

800

1000

Operation number
Figure 3.20. Comparison of momentum coupling coefficient

The data of consumed mass per one operation are shown in Figure 3.21. When 1000
V is applied, the amount of consumption in the case of normal propellant is 17 % lower
than another one. In the case of 750 V charge, similar as 1000 V charge case, consumed
mass of normal propellant is lower than perforated one, and its difference is 20.3 %. In
contrast, when 500 V is applied, the consumption of perforated propellant case is 23 %lower. This fact indicates the possibility that the ideal solid propellant shape exists
depending on supplied energy.

51Consumed mass of once operation [µg]

70
60
50
40
30
20
10
0
1000V

750V

500V

Supply voltage
Normal shape solid propellant

Perforated solid propellant

Figure 3.21. Comparison of consumed mass per one operation

Figure3.22 and 3.23 shows one kind of the frequency distribution examples. These
distribution graphs are classified by dividing from maximum value to minimum value by
10. As can be seen in these two figures, impulse bits of this experiment PPT are inclined
toward maximum value. This distribution indicates possibility that this PPT cannot be
evaluated simply by average value. Therefore, if we want to evaluate the PPT
performance in the future, evaluation should be carried out with maximum value andminimum value.
6

Data number

5
4
3
2
1
0

Class of impulse bit

Figure 3.22. Frequency distribution example (the case of normal solid propellant with 1000 V
charge)52

Data number

10
9
8
7
6
5
4
3
2
1
0

Class of impulse bit

Figure 3.23. Frequency distribution example (the case of perforated solid propellant
with 500 V charge)

For above facts, we can suppose one possibility that high effective electromagnetic
acceleration was performed in perforated solid propellant case with 500 V supply.
Naturally, if consumed surface area is decreased, consumed mass should also be
decreased. In addition, although theoretical impulse bits (which is calculated by current)of perforated propellant are same or moreover than normal propellant, actual measured
value of perforated one is lower. These facts probably indicate that electric energy was
supplied excessively in perforated solid propellant case of 1000 V and 750 V charge
because supply energy was same with normal propellant though consumed mass wasdecreased. As a result, excessively supply energy was consumed as internal energy andconverted heat energy, thus it cannot contribute to electromagnetic acceleration.
Furthermore, this heat energy generate radiation, and since it urged sublimation of solid
propellant by LTA, consumed mass per operation was increased. In the other hand, in thecase of 500 V charge, since supply energy was properly increased not to exceed until
limitation that each propellant particle can convert to kinetic energy, the impulse bit was
higher than normal shape solid propellant. Furthermore, for this reason, consumed massof perforated propellant was less than normal propellant because supply propellant massin perforated propellant case (which particles generate radiation energy) was lower.
Therefore, if the capacity of the capacitor is reduced to reduce the amount of total
electric energy or the total consumed mass area of the solid propellant is increased, theperformance as in the case of applying 500 V might be obtained even at a high voltage.

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Chapter 4: Conclusion
In order to gain a clue to improving the performance of Ablation-Fed Pulsed Plasma
Thruster, which is one kind of electric propulsion unit with solid propellant, theperformance of proceeded solid propellant, which is a new approach method, was verified.
Verification was carried out experimentally with comparison of normal shape solid
propellant and perforated solid propellant (perforated perpendicular to the consumption
surface). Each propellant was evaluated with three supply energy conditions (1000 V, 750
V and 500 V charge) by impulse bit measured with thruster stand, theoretical impulse bit
calculated by measured current value, consumed mass and momentum coupling
coefficient.
Firstly, we succeeded to operate PPT with perforated solid propellant and to measure
the impulse bit of that with thruster stand. In addition, discharge current from main
capacitor in PPT electrode was also measured with Rogowski coil.
Overall, the normal shape solid propellant with 1000 V charge indicated highest
thrust performance in impulse bit and momentum coupling coefficient. However, in thecase of perforated solid propellant, the characteristic properties that might exceed normal
propellant performance were obtained. At first, the transition of impulse bit. In the 1000
V charge experiment, impulse bit tended to decrease for both propellants. However, thetendency of perforated propellant is gentler, and if that tendency continues, the impulse
bit of perforated propellant will exceed after approximately 2000 operations. Thistendency is also indicated in the momentum coupling coefficient. On the other hand, themost characteristic result was obtained in the case of perforated solid propellant with 500
V charge. The normal propellant was similar to other voltages, and the transition of
impulse bit decreased. In contrast, perforated solid propellant with 500 V charge showed
the increasing tendency of impulse bit and momentum coupling coefficient. Although it
was lower than normal propellant at few times of operation, the impulse bit equivalent tonormal propellant was generated at 100 operations. In this experiment, unfortunately, themeasurement more operation times than this was not carried out due to the malfunctionof igniter, however, the possibility of impulse bit increasing was suggested.
Also in the result of consumed mass, perforated solid propellant with 500 V charge
indicated interesting property. In the case of 1000 and 750 V charge, the consumed massof normal propellant is lower than perforated propellant, however, at 500 V charge, theperforated propellant consumed mass was lower than the another. This difference in
consumed mass is 30.0 %, and this value can be supposed critical because the average
impulse bit of perforated propellant is 5.4 % lower than normal one.
For all of above results, almost supply electric energy was converted to heat energy
at 750 and 1000 V charge due to the excessive energy for solid propellant supply.
Therefore, even at high supply voltage, the performance similar to a 500 V charge
54perforated solid propellant might be obtained if the capacity of capacitor is decreased andtotal supply energy is reduced.
In the ablation-fed solid propellant pulsed plasma thruster, it is the general idea thatpropellant is mounted as much as possible to eliminate waste. However, as shown in the
result of this research, the solid propellant might have an optimal shape depending on theoperating supply power. Hence, it is necessary further verification of the hole shape, sizeand position.

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ACKNOWLEGEMENTS
I would like to thank Prof. Naoji Yamamoto who provided helpful comments andsuggestions.
I am also indebt to Dr. Hu Jing whose comments made enormous contribution to mypaper.
My completion of this thesis could not have been accomplished without the support ofProf. Wang Dong.
I also express my deep thanks to Kouichi Ushio, Masakazu Otubo, Kaartikey Misra,
Misaki Adachi, Shintaro Miyata for their kind support and advice.

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