# State-of-the-Art and Advancement Paths for Inductive Pulsed Plasma Thrusters

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## Abstract

**:**

## 1. Introduction

## 2. Review of Inductive Pulsed Plasma Thrusters

#### 2.1. Open Magnetic Flux Thrusters

#### 2.1.1. Planar Thrusters

#### 2.1.2. Conical Theta-Pinch Thrusters

#### 2.2. Closed Magnetic Flux Thrusters

#### 2.2.1. Field-Reversed Theta-Pinch FRCs

#### 2.2.2. Rotating Magnetic Field FRC Thrusters

#### Principle of Operation

#### Review of RMF-FRC Test Articles

#### Technical Obstacles to Testing

#### 2.2.3. Annular FRC Thrusters

#### 2.3. Summary of Experimental Data

## 3. Review of Modeling Techniques

#### 3.1. Open Magnetic Flux Thrusters

#### 3.1.1. Planar Thruster Modeling

#### 3.1.2. Conical Theta-Pinch Thruster Modeling

#### 3.2. Closed Magnetic Flux Thrusters

#### 3.2.1. Thruster Scaling Laws

#### Efficiency from Energy Conservation

#### Performance Metrics from Asymptotic Analysis of Equivalent Circuits

#### Challenges in Deriving Scaling Laws

#### 3.2.2. Equivalent Circuit Models

#### Equivalent Circuit Model for a Stationary Plasmoid

#### Calibrated Equivalent Circuit Model to Estimate Energy Deposition in FRC

#### Circuit Model for Second Stage Acceleration of an FRC Plasmoid

#### Equivalent Circuit Model for FRC Translation including RMF Coils

#### Equivalent Circuit Model for Annular FRC Translation

#### Challenges with Equivalent Circuit Modeling

#### 3.2.3. High-Fidelity Models

#### Magnetohydrodynamic (MHD) Fluid Models

#### Two-Fluid Models

#### Kinetic Models

#### High Fidelity Modeling Challenges

## 4. Review of Major Subsystems

#### 4.1. Power

#### 4.1.1. Power Processing Units

#### EMPT and ELF Thruster PPU

#### UM RMF-FRC PPU

#### 4.1.2. Discharge Circuit

#### Discharge Circuit Topologies

#### Inductive Energy Recapture

#### Switches

^{®}rated up to 9 kA of peak current. Later testing used a distributed array of smaller, higher efficiency IGBTs made by IXYS

^{®}. The faster switching times of both IGBT models enabled the EMPT to achieve the first reported multi-pulse operation of an IPPT at multi-kHz repetition rates [47]. Paralleling of multiple high power IGBTs was found to enable peak discharge currents up to 20 kA in the 30 kW ELF thruster [85].

#### Capacitors

#### 4.2. Drive Coil

#### 4.3. Propellant Management and Injection

#### 4.4. Preionization

#### 4.5. Cooling

#### 4.6. External Fields

## 5. Advancement Paths: Modeling

#### 5.1. Formation Physics

#### 5.1.1. IPPT Current Sheet Formation

#### Key Physics and Requirements for Current Sheet Formation

#### Current Sheet Formation Scaling to Lower Energy per Pulse

#### Propellant Mass and Energy Loss during Current Sheet Formation

#### Current Sheet Stability on Formation and Acceleration Timescales

#### 5.1.2. FRC Formation

#### Key Physics and Requirements for FRC formation at Low Discharge Energy

#### Propellant Mass and Energy Losses During FRC Formation

#### 5.2. Acceleration Physics

#### 5.2.1. Identification and Scaling of Dominant Acceleration Mechanisms

#### 5.2.2. Influence of Changing Plasma Geometry on Inductive Acceleration

#### 5.3. Molecular Propellant Physics

#### 5.3.1. Influence of Plasma Chemistry on the Design and Scaling of IPPTs

#### 5.3.2. Importance of Recombination in the Presence of Large Temperature Gradients

#### 5.4. Effects of Asymmetric Charge Exchange Reactions

## 6. Advancement Paths: Major Subsystems

#### 6.1. Power

#### 6.1.1. Discharge Circuit

#### Discharge Circuit Topology

#### Inductive Energy Recapture

#### Capacitors

#### Switches

^{10}pulses) expected over the course of a typical mission. Encouragingly, failure in time (FIT) rates for modern IGBTs in terrestiral applications are typically on the order of ${10}^{-9}$ failures per device-hour [110,111]. While promising work by Kirtley et al. [85,86] demonstrated IGBT operation in excess of 10

^{9}pulses in benchtop PPU endurance testing efforts, it must be confirmed that this longevity can be replicated in an actual thruster. In addition, care should be exercised when attempting to broadly extend these findings, since switches in different IPPTs may be subjected to vastly different operating conditions. Extended lifetime testing of a wide range of solid-state switches, either as part of broader IPPT lifetime testing or under conditions meant to closely replicate IPPT operation, should be conducted before these devices can be considered to possess sufficient lifetime. Detailed reliability models for solid-state switches operating in a relevant space environment will likely need to be developed with a focus on identifying critical switch failure modes. The inclusion of realistic thermal and power cycling will be important when developing these models, since switch reliability and lifetime are critically impacted by these factors [110]. Moreover, implementation of condition monitoring systems is recommended so the performance and state of the devices over the course of lifetime testing can be carefully recorded, allowing for more accurate quantification of the risk of device failure.

#### IPPT PPUs

#### 6.1.2. Circuit Modeling

^{®}.

#### 6.2. Propellant Injection

#### 6.3. Preionization

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Schematic showing the basic operation of a planar IPPT, where the Lorentz body force $\mathbf{f}$ in the axial direction arises from the interaction between the azimuthal plasma current density $\mathbf{j}=-{j}_{p}\widehat{\theta}$ and the radial magnetic field $\mathbf{B}={B}_{r}\widehat{r}$. (

**b**) Sample discharge current from the PIT MK Va for one of the nine parallel coils (from [9]).

**Figure 2.**PIT MK V and MK Va Marx-generator coil configuration: (

**a**) one complete Marx-generator loop and (

**b**) the nine complete loops comprising the entire coil (from [3]).

**Figure 3.**Schematic showing a typical propellant injection scheme employed on the PIT (from [3]).

**Figure 4.**(

**a**) Specific impulse and (

**b**) thrust efficiency as a function of specific energy for the PIT MK Va thruster operating on ammonia propellant (data from [3]).

**Figure 6.**Schematic showing the basic operation of an open magnetic flux conical theta-pinch inductive pulsed plasma thruster. The Lorentz body force $\mathbf{f}$, with components in the radial axial directions, arises from the interaction between the azimuthal plasma current density $\mathbf{j}=-{j}_{p}\widehat{\theta}$ and the radial and axial magnetic field components $\mathbf{B}={B}_{r}\widehat{r}+{B}_{z}\widehat{z}$.

**Figure 7.**Schematic illustrations of conical coil sets containing (

**a**) a spheromak plasma and (

**b**) a field-reversed configuration (FRC) plasma, showing the directional sense of the current in the coils, the azimuthal plasma current ${j}_{p}$, and poloidal magnetic field ${B}_{pol}$, the magnetic field external to the plasma ${B}_{ext}$, and the toroidal magnetic field ${B}_{tor}$ in the spheromak configuration.

**Figure 8.**Schematic showing field-reversed theta pinch formation for closed magnetic flux thrusters: (

**a**) preionization plasma is introduced into a background magnetic field; (

**b**) a strong pulse of current generates a time-dependent magnetic field with polarity opposing the initial background magnetic field that compresses the plasma both radially and axially; (

**c**) a closed magnetic field structure confines the plasma within a separatrix that divides the forward and reverse fields; and (

**d**) magnetic field gradients in the axial direction accelerate and eject the resulting plasmoid (Reproduced/modified from [29]; with the permission of AIP Publishing.).

**Figure 10.**RMF-FRC Operation—(

**a**) Side view cross-section in the r-z plane of the thruster illustrating how ionized gas is injected into the discharge chamber. A steady bias magnetic field with radial gradient is present. (

**b**) End-on view of the thruster in the r-$\theta $ plane depicting two sets of coils oriented in the x- and y-directions that generate a rotating magnetic field (RMF) by using sinusoidal currents at frequency $\omega $ applied 90° out of phase. The RMF induces axial and azimuthal currents. (

**c**) Side view of the r-z plane illustrating FRC formation. Large azimuthal currents form the plasmoid and interact with the external radial magnetic field component to axially accelerate the plasmoid via a Lorentz body force.

**Figure 11.**RMF-FRC test articles: (

**a**) Schematic of Tokyo University electrodeless helicon plasma thruster (from [45]; licensed under a Creative Commons Attribution (CC BY) license), (

**b**) MSNW electromagnetic plasma thruster (from [47]; reproduced with permission of the author), (

**c**) Air Force Research Laboratory RP3-X thruster (from [49]), (

**d**) MSNW electrodeless Lorentz force thruster (from [51]; reproduced with permission of the author), (

**e**) CAD model of the University of Michigan RMF thruster (from [43]; reproduced with permission of Electric Rocket Propulsion Society).

**Figure 12.**Diagram of an AFRC thruster (from [53]).

**Figure 13.**XOCOT-T3 experiment (from [54]; reproduced with permission of the author).

**Figure 14.**Circuit models: (

**a**) general lumped-element representation of an IPPT and (

**b**) equivalent circuit (after [16]).

**Figure 15.**Magnetic flux contours calculated with QuickField for a coil with six two-turn leads in parallel and a cone angle of 60°. The plasma thickness is 1 cm. The overall dimensions of the coil are similar to the FARAD coil of Ref. [73].

**Figure 16.**(

**a**) Geometry used to model the coil and plasma coupling in Ref. [75], (

**b**) current waveforms of an ELF discharge with and without a plasma in the thruster (from [51]; reproduced with permission of the author), (

**c**) equivalent circuit model of an RMF-FRC with flux conservers (from [43]; reproduced with permission of Electric Rocket Propulsion Society).

**Figure 17.**Equivalent circuit model of an AFRC (from [54]; reproduced with permission of the author).

**Figure 18.**Numerical simulations of FRC thrusters: (

**a**) Moqui simulation showing acceleration of a plasmoid using sequentially pulsed magnets (from [80]; reproduced with permission of Electric Rocket Propulsion Society), (

**b**) SEL-HiFi simulation shows neutral entrainment by a translating FRC (from [81]; reproduced with permission of the author).

**Figure 19.**Diagram illustrating the location and role of the PPU in stepping-up the voltage for an IPPT capacitor bank.

**Figure 20.**Simplified circuit diagram of the pulse charging PPU used to recharge the capacitor bank of the ELF thruster during continuous operation (based on schematic from [86]).

**Figure 21.**The ELF J6 PPU (from [86]).

**Figure 22.**Mechanical design of a single PPU to supply power to one antenna in the UM 30 kW RMF-FRC (from [43]; reproduced with permission of Electric Rocket Propulsion Society). The low-pass filter for protecting the input source from switching transients is not pictured.

**Figure 23.**Simulated underdamped, critically damped, and overdamped $RLC$ discharge circuit waveforms for the capacitor voltage and current.

**Figure 25.**Pulse compression ring (

**a**) circuit schematic and (

**b**) current and voltage waveforms at each of the three capacitors (Reproduced/modified from [89]; with the permission of AIP Publishing)

**Figure 26.**Example current waveform and IPPT discharge circuit schematic incorporating an IGBT for full-cycle inductive energy recapture.

**Figure 27.**Illustration of a two-turn Archimedes spiral coil with six parallel leads clocked at 60° intervals, indicated by the colors red, orange, green, blue, purple, black. Each lead completes one outward counter-clockwise spiral on the front surface (solid line) and then one inward counter-clockwise spiral on the back surface (dashed line) to return to the initial starting point.

**Figure 28.**(

**a**) A proposed Halbach array-based design for a drive coil and (

**b**) computed flux contours for the proposed configuration (from [93]; reproduced with permission of the author).

**Figure 29.**Continued flow of current after end of second half cycle in the UW HiPeR-PIT discharge circuit, resulting in voltage ringing and loss of charge from the energy storage capacitors.

**Figure 30.**(

**a**) General isolated full bridge resonant CCPS topology and (

**b**–

**e**) popular resonant tank circuit options as denoted (note: many other resonant CCPS variations are possible).

**Figure 31.**Simplified circuit diagram of the UW HiPeR-PIT PPU designed to enable thruster operation at repetition rates from 1 kHz to 10 kHz.

**Figure 32.**Simulated waveforms of the main bank voltage (${V}_{mb}$) and currents through the main bank (${I}_{mb}$ and each of the boost switches (${I}_{b,sw}$), inductors (${I}_{b,L}$), and diodes (${I}_{b,D}$) in the UW HiPeR-PIT PPU.

**Figure 33.**Example of a functional physics model for an IGBT with circuit elements superimposed (from [116]).

**Table 1.**Summary of operating parameters and test data for various IPPTs. (* data not available, ** equivalent circuit voltage, *** equivalent circuit current, ${}^{+}$ estimated value, ${}^{++}$ not applicable).

Experiment | ${\mathit{I}}_{\mathbf{sp}}$ [s] | ${\mathit{I}}_{\mathbf{bit}}$ [mN-s] | ${\mathit{\eta}}_{\mathbf{t}}$ [%] | ${\mathit{B}}_{\mathbf{pk}}$ [T] | $\u2329\mathit{\beta}\u232a$ | ${\mathit{V}}_{0}$ [kV] | ${\mathit{I}}_{\mathbf{pk}}$ [kA] |
---|---|---|---|---|---|---|---|

PIT MK Va (open flux) [3] | 2000–7000 | 50–120 | 40–55 | 0.55 | ${}^{++}$ | 30–32 ** | 135 *** |

CTP-IPPT (open flux) [4] | 1000–4500 | 0.1–1 | <6 ${}^{+}$ | * | ${}^{++}$ | 5 | 18 |

MSFC-IPPT (open flux) [18] | * | * | * | * | ${}^{++}$ | 3 | 7.4 |

PTX (closed flux) [35] | * | * | * | 0.5 | * | 35 | 50 |

PT-1 (closed flux) [36] | * | * | * | 0.1 | * | 3 | 14 |

1 kW EMPT (closed flux) [47] | * | * | * | 0.03 | ∼0.5 | 1.3 | 1 |

50 J/pulse ELF (closed flux) [51] | * | 0.4 | * | 0.04 | ∼0.5 | 10 | * |

30 kW ELF (closed flux) [58] | * | * | * | 0.01 | ∼0.5 | 3 | 3 |

**Table 2.**Representative circuit parameters for selected IPPTs. (* estimated values, ** value not reported).

Thruster | ${\mathit{C}}_{\mathit{m}\mathit{b}}$ | ${\mathit{L}}_{\mathit{c}}$ | ${\mathit{L}}_{\mathit{s}\mathit{t}\mathit{r}\mathit{a}\mathit{y}}$ | ${\mathit{V}}_{0}$ | ${\mathit{I}}_{\mathit{m}\mathit{a}\mathit{x}}$ | $\mathbf{dV}/\mathbf{dt}$ | $\mathbf{dI}/\mathbf{dt}$ |
---|---|---|---|---|---|---|---|

[$\mathsf{\mu}$F] | [nH] | [nH] | [kV] | [kA] | [kV/$\mathsf{\mu}$s] | [kA/$\mathsf{\mu}$s] | |

PIT MK Va [3,65] | 9 | 680 | 60 | 30 | 135 | 11 | 270 |

FARAD [17,87] | 20 | 810 | 70 | 3.1 | 10* | 1.2 | 45 |

MSFC IPPT [18] | 10 | 705 | 336 | 3 | 7 | 0.7 | 2 |

ELF-160 [88] * | 1.32 | 325 | ** | 3.4 | 7 | 5 | 10 |

**Table 3.**Comparison of characteristics of selected solid-state switch types. Note that the designations in this table are for individual switches and not for arrays containing multiple switches.

Parameter | Thyristor/SCR | IGBT | MOSFET |
---|---|---|---|

Switching Speed | Slowest | Intermediate | Fastest |

Current | Highest | Intermediate | Lowest |

Breakdown Voltage | Highest | Intermediate | Lowest |

Control Type | Current | Voltage | Voltage |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Polzin, K.; Martin, A.; Little, J.; Promislow, C.; Jorns, B.; Woods, J.
State-of-the-Art and Advancement Paths for Inductive Pulsed Plasma Thrusters. *Aerospace* **2020**, *7*, 105.
https://doi.org/10.3390/aerospace7080105

**AMA Style**

Polzin K, Martin A, Little J, Promislow C, Jorns B, Woods J.
State-of-the-Art and Advancement Paths for Inductive Pulsed Plasma Thrusters. *Aerospace*. 2020; 7(8):105.
https://doi.org/10.3390/aerospace7080105

**Chicago/Turabian Style**

Polzin, Kurt, Adam Martin, Justin Little, Curtis Promislow, Benjamin Jorns, and Joshua Woods.
2020. "State-of-the-Art and Advancement Paths for Inductive Pulsed Plasma Thrusters" *Aerospace* 7, no. 8: 105.
https://doi.org/10.3390/aerospace7080105