Plasma thrustersSEMINAR FOR THE MASTER IN NUCLEAR, PARTICLE AND ASTRO PHYSICS, DEPARTMENT OF PHYSICS, TECHNISCHE UNIVERSITÄT MÜNCHEN, GERMANY (WS 2015/2016)BY T IZ IANO FULCERI

Structure of the seminar• Motivation• Rocket principle and momentum equation• Power, thrust, specific impulse• Case analysis: Constant power and thrust, prescribed mission time• Plasma thrusters as a subset of electric propulsion systems• Physics of plasma propulsion• HET (Hall Effect Thruster)• MPD (Magnetoplasmadynamic) Thruster• VASIMR (Variable Specific Impulse Magnetoplasma Rocket)• ELF Thruster (Electrodeless Lorentz Force Thruster)• Conclusions and prospects• References

MotivationPlasma thrusters are researched and developed as a solution for the following fields of application:• Precise trajectory corrections for satellites and/or probes• In-space robotic probe propulsion (example ESA SMART-1)• In-space manned spacecraft propulsion to Mars (proposed)• Propulsion in outer Solar System (beyond Jupiter’s orbit)All of which require (or will require) high fuel efficiency (see later: Isp), long lifespan, and a small thruster mass.

Rocket principle and momentum equation

𝑝 (𝑡 )=𝑀 (𝑡 )𝑣 (𝑡 )+∫0

𝑡

�̇� (𝑡 ′ ) [𝑣 ( 𝑡′ )−𝑐 (𝑡′ ) ]𝑑𝑡 ′

• p(t) = Total momentum of the system (rocket + propellant)• M(t) = Mass of the rocket + mass of unexpended propellant or “wet

mass”• v(t) = Rocket velocity• = Mass flow of the propellant• c(t) = Jet velocity

Thrust, Power, Specific Impulse

𝑝 (𝑡 )=𝑀 (𝑡 )𝑣 (𝑡 )+∫0

𝑡

�̇� (𝑡 ′ ) [𝑣 ( 𝑡′ )−𝑐 (𝑡′ ) ]𝑑𝑡 ′

Thrust:

Calculating the thrust (accelerating force on the rocket structure) in a vacuum:Total momentum change of the system (rocket + propellant) must be zero:

Thrust, Power, Specific Impulse

𝐸𝑘=12𝑀𝑣2+∫

0

𝑡 12�̇� ( 𝑡′ ) [𝑣 (𝑡′ )−𝑐 (𝑡 ′) ]2𝑑𝑡 ′

Kinetic power:

From the kinetic energy of the total system (rocket + propellant), we can calculatethe kinetic energy per unit time (kinetic power) of the exhaust jet:

Thrust, Power, Specific Impulse

PRIMARY POWER SOURCE

Produces thermal or electric power:

THRUSTERConverts primary power to kinetic

power of the propellant with

efficiency η:

EXHAUST JETProduces the

acceleration of the rocket:

A rocket propulsion system can be generally understood as follows:

Thrust, Power, Specific ImpulseUntil now we have the following quantities:

• Thrust: • Kinetic power: We can define another useful quantity, specific impulse, which measures how much momentum is produced per unit mass (or weight) of expended propellant:

Where is the standard gravitational acceleration at sea level.The two definitions are interchangeable:

Case analysis: Constant power and thrust, prescribed mission time

The can be calculated as follows:

This means also that

Electric thruster starting with mass , operating for a time , of jet speed , such as toaccomplish and equivalent (force-free) velocity change of .

We are looking for the final mass of the rocket (which is the mass at the end of the mission)

Plasma thrusters as a subset of electric propulsion systems

Spac

e pr

opul

sion

Chemical propulsion

Liquid propellant

Solid propellant

Hybrid

Electric propulsion

Electric thrusters

Electrothermal thrusters (resisto-

jet)

Arc-jet thrusters

Electromagnetic thrusters

Ion thrusters

Plasma thrusters

HET

MPD

VASIMR

ELF

Others…

Physics of Plasma Propulsion

• We deal with thrust generation, so we are interested in the momentum equation for each species j:

Physics of Plasma Propulsion

• For further analysis of the possible accelerating processes we make the following assumptions:• Only two fluids: ions and electrons• Most important assumption: the working fluid (propellant) is an electrically

conducting medium which remains quasi-neutral • The collision terms will therefore describe collisions between ions and electrons:

• Anisotropic component of the pressure tensor negligible, so that reduces to • Ion and electron velocities can be related in terms of current as follows: • Inertial term on the left side of the electron equation negligible due to small

electron mass

Physics of Plasma Propulsion• Useful definitions:• Conductivity: • Hall parameter: • Electron cyclotron frequency:

• The momentum conservation equations for the ionic and the electronic components becomes:

Physics of Plasma Propulsion• We can define the following useful quantity:

which represents the electric field in a reference frame in motion with the average heavy particle flow plus the electron pressure gradient contribution.• We can rewrite the expression for the current:

which can be recognized as the generalized Ohm’s law (relationship between the fields and the currents in a plasma)

Physics of Plasma Propulsion• With further hypotheses we arrive at the following equation for

the motion of the working fluid:

• All types of plasma thrusters are based on one or more of the above effects included in this equation:• Arc-jet thrusters are totally based on pressure gradients• Ion thrusters are based on an externally generated E-field• MPD thrusters are based mainly on the collisional contribution

from the electron component• HET thrusters are based on the self-consistent E-field

associated with the Hall effect

Hall Effect Thruster (HET)Parameter ValueTypical thrust 10 -80 mNTypical specific impulse

1000-8000 s

Typical power 1 kW to 100 kW

Efficiency 70-80%

Hall Effect Thruster (HET)Principle of operation

1. Steady-state Radial Magnetic Field (B) produced by electromagnets (0.02-0.03 T)

2. Injection of positively ionized propellant (usually Xenon) and at the same time emission of electrons from the cathode.

3. An axial electric field (E) arises because of the charge separation.

4. The electrons, having less inertia that the ions react faster to the E-field and drift towards the propellant channel.

5. The electrons have now an axial velocity v, which is perpendicular to the radial B-field.

6. The vxB force (“Hall effect” on currents, “Lorentz force” on particles) traps the electrons on a circular path at the end of the propellant channel (current density j), making them act as a suspended negative electrode.

7. The ions are accelerated towards the electron cloud reaching velocities in the order of 10 to 80 km/s, they neutralize and carry momentum away providing thrust to the structure.

Magnetoplasmadynamic (MPD) thruster

Parameter ValueTypical thrust 2.5-25 NTypical specific impulse

2000 s

Typical power 100-500 kWEfficiency 40-60%

Magnetoplasmadynamic (MPD) thrusterPrinciple of operation

1. Voltage is applied between the central and the external electrode

2. The propellant is injected between the two electrodes

3. The voltage between the electrodes is sufficient to ionize the propellant and generate a discharge with a radially directed current distribution

4. The radial current produces an azimuthal magnetic field B

5. The magnetic field B is perpendicular to the current by which it is generated, this creates a jxB force density per unit length of the discharge on both ions and electrons, independent of the charge sign.

6. The ionized propellant is pushed away by the jxB force, producing thrust on the structure

Variable Specific Impulse Magnetoplasma Rocket (VASIMR)

Parameter ValueTypical thrust 5 NTypical specific impulse

5000 s (optimal)

Typical power (VX-200)

200 kW

Efficiency 70%

Variable Specific Impulse Magnetoplasma Rocket (VASIMR) – Principle of Operation

1. Propellant is injected in the ionization chamber

2. The Helicon antenna ionizes the propellant, which becomes a plasma

3. Superconducting coils confine the plasmaThe plasma is heated to about 1MK by an Ion Cyclotron Frequency antenna

4. The hot plasma drifts toward the lower magnetic field region away from the thruster

5. The reaction is felt on the structure as thrust

Electrodeless Lorentz Force (ELF) Thruster

Parameter ValueTypical thrust 1N (pulsed)Typical specific impulse

1000-6000 s

Typical power 50kW (pulsed)

Efficiency >50%

Electrodeless Lorentz Force (ELF) ThrusterPrinciple of Operation

• Electromagnets wound around the propellant channel produce a steady-state axial magnetic field decreasing in intensity in the outward direction

• Propellant is pre-ionized and injected in the channel

• A Rotating Magnetic Field is produced by two pairs of coils excited with two identical sinusoidal waveforms which are out of phase by 90°

• The RMF, induces an azimutal electric current in the propellant j_theta

• The RMF driven currents, coupled with the large axial magnetic field gradient produced inside the conically shaped flux-conserving thruster, produce a large axial JθxBr force that accelerates the plasmoid to high velocity. The axial force is thus overwhelmingly determined by the driven Jθand resultant Br rather than thermal expansion forces, maximizing thrust efficiency.

Conclusions and prospects• Plasma thrusters are a promising research field• Some plasma thruster types already demonstrated their utility• There is a wide range of methods, configurations and

mechanisms to accelerate a plasma propellant (we did not cover all of them)• In the near future we should expect an increased interest in

this kind of technology• The physics of this systems is not very well understood: this is

an opportunity for both applied and theoretical physics

Special: Fusion Plasma ThrustersFusion Driven Rocket (FDR)

Special: Fusion Plasma ThrustersFlow-Stabilized Z-Pinch Fusion Space Thruster

“Specific impulses in the range of 10^6s and thrust levels of 10^5 N

are possible.”

References• Lecture notes from the 2004 MIT course «Rocket Propulsion» by Prof. Manuel Martinez-

Sanchez• «Rocket and Spacecraft Propulsion» by Turner, Martin J. L. Chapters 2 and 6• «Magnetoplasmadynamic Thrusters» fact sheet from NASA’s website (

http://www.nasa.gov/centers/glenn/about/fs22grc.html)• «An analysis of current propulsion systems» (

http://currentpropulsionsystems.weebly.com/electromagnetic-propulsion-systems.html)• «Fundamental scaling law for electric propulsion concepts» by M.Andreucci, L.Biagioni,

S.Marcuccio, F.Paganucci - Alta S.p.a., Pisa, Italy• «Development Toward a Spaceflight Capable VASIMR Engine and SEP Applications» by J.P.

Squire, M.D.Carter, F.R. Chang Diaz, M.Giambusso, A.V.Ilin, C.S. Olsen – Ad Astra Rocket Company, Webster, Texas, USA and E.A.Bering, III – University of Houston, Houston, Texas, USA

• «Pulsed Plasmoid Propulsion: The ELF Thruster» J.Slough and D.Kirtley – MSNW, Redmond, WA, USA

• “The Fusion Driven Rocket” PI: J.Slough, A.Pancotti et. al.• “Advanced Space Propulsion Based on the Flow-Stabilized Z-Pinch Fusion Concept”

U.Shumlak et. al. – Aerospace & Energetics Research Program, University of Washington, Seattle, WA, USA (https://www.aa.washington.edu/research/ZaP/research/plasmaOverview)

Pictures• http://

www.popsci.com/technology/article/2010-10/123000-mph-plasma-engine-could-finally-take-astronauts-mars

• http://www.engadget.com/2015/04/01/how-ion-thruster-technology-will-power-future-nasa-missions/

• http://htx.pppl.gov/ht.html• Title picture: http://

www.irs.uni-stuttgart.de/forschung/elektrische_raumfahrtantriebe/triebwerke/mpd-tw/fremdfeldbeschl-tw/mpd-afmpd.html

• Index picture: http://web.stanford.edu/group/pdl/• Alta Space (now part of Sitael) website: www.alta-space.com• Ad Astra website: http://www.adastrarocket.com/aarc/• MSNW space propulsion website: http://

msnwllc.com/space-propulsion