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Mario Merino Martínez – Universidad Politécnica de MadridMagnetic Nozzles for Plasma Space Propulsion – YAEY 2010

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Magnetic Nozzles for Plasma Space Propulsion

Mario Merino MartínezUniversidad Politécnica de Madrid


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Contents

• About this Project

• Key aspects of Electric Propulsion

• Magnetic Nozzles

• Physical and Mathematical Modeling

• Numeric Integration and Simulation

• Main Results

• (Other) Conclusions


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About this Project• PSP research group at UPM

http://web.fmetsia.upm.es/psp/

• Main Objectives:1. Gain understanding: MN physics, review SoA

2. Develop a robust physical-mathematical model of the MN

3. Implement model in a computer program and simulate

4. Study and analyze:• Acceleration mechanisms and relevant physics of the expansion

• Influence of the main control parameters

• Existence and role of electric currents inside the plasma

• Propulsive performances and plume efficiency of the nozzle

• Role of electron thermodynamics in the jet development


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Key aspects of Electric Propulsion

Thermoelectrical Electrostatic Electromagnetic


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Magnetic Nozzles• What are MN? Physical description• What do they do? Guide, expand,

accelerate a plasma jet• Similarities with a traditional, solid

nozzle (de Laval):– Convergent-Divergent geometry– Sonic conditions at the throat (ions)– Different physics, mechanisms

• Any advantage over de Laval Nozzles?– Wall-plasma contact is avoided– “Throttlability”: Thrust and Isp

continuous control by changing field intensity and geometry

• Other applications: Advanced Manufacturing Systems

• Issues may exist: Magnetic detachment downstream


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Main Thrusters using MN• Applied-Field MPD Thruster:

– More protected electrodes– Greater performances, efficiency– Different acc. mechanisms identified

• Helicon Thruster– High density plasma. Some studies

point to the existence of a small fraction of hot electrons interesting propulsive advantages

• VASIMR– Magnetic Mirror effects– Helicon Source + ICRH + MN– Isp & thrust control through MN

• Diverging Cusped Field Thruster (MIT)– Similar to HET, avoids wall erosion to

large extent– Formation of magnetic bottles at cusps


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Description of the Model

• Develop a physically-coherent two-dimensional model to characterize expansion & acceleration, study electric current formation, analyze the influence of control parameters, and assess plume efficiency of the MN

Magnetic field created by a single current loop


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Main Hypotheses of the Model

• Axisymmetric and quasi-stationary flow

• Completely ionized (no neutrals), collisionless plasma

– Ions (Single-charged) and electrons treatedas two independent, interpenetrating fluid species

• Quasineutrality is fulfilled

• Electron inertia neglected

• Cold ions (ion pressure neglected)

• Electrons are completely magnetizedin the region under study

• Any degree of ion magnetization

• Electrons are treated as an isothermal or a polytrophic species

• Plasma self-induced magnetic field neglectedvs applied field

• No net electric current in the plasma jet


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( )

Electron equations

• Isothermalelectrons:

• Polytrophicelectrons:


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Ion Equations

• Continuity Eq., using electron Mom. Eq.:

• Ion Momentum Eq.:


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Control Parameters

• Model can be made dimensionless:

• Control parameters:


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Numeric Integration and Simulation

• 3 pde’s Necessity toemploy numeric methods

• M.O.C. reduces them to3 ode’s alongcharacteristic lines

• Predictor-Correctorsscheme furtherreduces themto 3 de’s

• DiMagNo 2D code is fastand accurate – first of itskind devoted to MN


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DiMagNo 2D Integration Algorithm

• Spatial discretization, advance logic

• Three types of points:– Initial (Euler) projection and intersection of

Characteristics

– Calculation of new-point properties

– Line readjustment and property recalculation with Runge-Kutta 2

• Frontline advancement and Characteristic linespropagation, forming a mesh

• Code is modular and extensible


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Results: Initially uniform Jet

• Two nozzles (long, left; short, right)

• Mach number• Density and potential• 1D Model (red lines)

used to validate results• Density focalization• Isothermal electrons:

Potential – ∞

• Ion magnetization (see below) decreases radial gradients.

Solid: 0.1Dashed: 10Dash-and-dot: 100


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Results – Initially non-uniform jet

• Mach Number and Potential profiles are similar – differences occur mainly in the outer sl. similar performances expected

• Much larger radial density gradient throughout the MN

Solid: 0.1Dashed: 10Dash-and-dot: 100


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Results: Effects of Ion Magnetization

• Partial Ion magnetizationcauses ion and electronstreamtubes to separate:

Longitudinal electriccurrents do arise

Ions are put into rotation(although the azimuthalcurrent they generate isnegligible)


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Results: The role of the Hall Current

• Magnetic force exerted on the plasma per unit volume:

• Initially uniform jet:– No azimuthal electron currents exist inside the plasma volume, but a

current sheet develops at the plasma-vacuum transition: all Hall current – and magnetic force – is concentrated there

• Initially non-uniform jet:– Maximal Hall current takes place inside the jet. A relative

displacement of this maximum toward the axis takes place due to density focalization Maximal magnetic force behaves likewise


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Results: Nozzle Performances and Efficiency

• Delivered Thrust gain (and Isp) depend mainly onnozzle shape and initial radial gradients

• Ion kinetic power is almost insensitive to radial gradients

• 2D model allows to obtain plume efficiency(radial losses due to divergence):

– Initial gradients, low ion magnetization and slowly diverging, long nozzles provide bestefficiencies


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Results: Electron Thermodynamics (Polytrophic)

• Blue line: isothermal 1D• Greater Mach numbers are

reached as the temperature falls, especially at the outer sl. (but lower ion velocities)

• Greater influence of ion magnetization

• Density profiles and currents are similar

• Electric potential has an asymptote:


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(Other) Conclusions

• Non-negligible longitudinal electric currents exist Current ambipolarity condition not fulfilled

• In general, most kinetic energy of the jet has a thermoelectric origin, but there exists also a electromagnetic contribution (extracted from the magnetic circuit currents)

• Polytrophic electrons yield lower thrust, but higher plume efficiency

• Ion magnetization should be kept to a minimum, since it spoils efficiency and hinders magnetic detachment downstream

• Preliminary detachment studies (not discussed here) reveal the importance of the Hall currents


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Future research lines

• Include two or more electron populations at different temperatures (related to Helicon Thrusters) Done: hot&cold electrons can bring large improvements of propulsive performances!

• Include resistivity (collisions),electron inertia, and self-induced magnetic field, to assess the three main envisioned detachment mechanisms Our current work deals with this

• Allow special ion distribution functions, to better study MN of the VASIMR

• Extend the applicability of the DiMagNo2D code to other fields (traditional nozzles, reentry capsule flows, etc.)


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Conferences and Published Articles

1. E. Ahedo and M. Merino, “Two-dimensional plasma acceleration in a divergent Magnetic Nozzle”, 45th Joint Propulsion Conference, Denver, CO, AIAA 2009-5361, 2–5 August 2009.

2. E. Ahedo and M. Merino, “Acceleration of a focused plasma jet in a divergent Magnetic Nozzle”, 31st International Electric Propulsion Conference, University of Michigan, USA, September 20–24, 2009.

3. E. Ahedo, M. Merino, “Two-dimensional supersonic expansion of a plasma jet in a divergent Magnetic Nozzle”, Physics of Plasmas (2010; accepted for publication).

4. M. Merino, E. Ahedo, “Two-Dimensional Magnetic Nozzle Acceleration of a Two-Electron Component Plasma”, 2nd Space Propulsion Conference, 3–6 May 2010, San Sebastian, Spain.


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