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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
Mario Merino Martínez – Universidad Politécnica de MadridMagnetic Nozzles for Plasma Space Propulsion – YAEY 2010
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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
Mario Merino Martínez – Universidad Politécnica de MadridMagnetic Nozzles for Plasma Space Propulsion – YAEY 2010
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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
Mario Merino Martínez – Universidad Politécnica de MadridMagnetic Nozzles for Plasma Space Propulsion – YAEY 2010
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Key aspects of Electric Propulsion
Thermoelectrical Electrostatic Electromagnetic
Mario Merino Martínez – Universidad Politécnica de MadridMagnetic Nozzles for Plasma Space Propulsion – YAEY 2010
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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
Mario Merino Martínez – Universidad Politécnica de MadridMagnetic Nozzles for Plasma Space Propulsion – YAEY 2010
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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
Mario Merino Martínez – Universidad Politécnica de MadridMagnetic Nozzles for Plasma Space Propulsion – YAEY 2010
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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
Mario Merino Martínez – Universidad Politécnica de MadridMagnetic Nozzles for Plasma Space Propulsion – YAEY 2010
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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
Mario Merino Martínez – Universidad Politécnica de MadridMagnetic Nozzles for Plasma Space Propulsion – YAEY 2010
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( )
Electron equations
• Isothermalelectrons:
• Polytrophicelectrons:
Mario Merino Martínez – Universidad Politécnica de MadridMagnetic Nozzles for Plasma Space Propulsion – YAEY 2010
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Ion Equations
• Continuity Eq., using electron Mom. Eq.:
• Ion Momentum Eq.:
Mario Merino Martínez – Universidad Politécnica de MadridMagnetic Nozzles for Plasma Space Propulsion – YAEY 2010
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Control Parameters
• Model can be made dimensionless:
• Control parameters:
Mario Merino Martínez – Universidad Politécnica de MadridMagnetic Nozzles for Plasma Space Propulsion – YAEY 2010
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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
Mario Merino Martínez – Universidad Politécnica de MadridMagnetic Nozzles for Plasma Space Propulsion – YAEY 2010
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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
Mario Merino Martínez – Universidad Politécnica de MadridMagnetic Nozzles for Plasma Space Propulsion – YAEY 2010
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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
Mario Merino Martínez – Universidad Politécnica de MadridMagnetic Nozzles for Plasma Space Propulsion – YAEY 2010
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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
Mario Merino Martínez – Universidad Politécnica de MadridMagnetic Nozzles for Plasma Space Propulsion – YAEY 2010
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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)
Mario Merino Martínez – Universidad Politécnica de MadridMagnetic Nozzles for Plasma Space Propulsion – YAEY 2010
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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
Mario Merino Martínez – Universidad Politécnica de MadridMagnetic Nozzles for Plasma Space Propulsion – YAEY 2010
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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
Mario Merino Martínez – Universidad Politécnica de MadridMagnetic Nozzles for Plasma Space Propulsion – YAEY 2010
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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:
Mario Merino Martínez – Universidad Politécnica de MadridMagnetic Nozzles for Plasma Space Propulsion – YAEY 2010
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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
Mario Merino Martínez – Universidad Politécnica de MadridMagnetic Nozzles for Plasma Space Propulsion – YAEY 2010
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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.)
Mario Merino Martínez – Universidad Politécnica de MadridMagnetic Nozzles for Plasma Space Propulsion – YAEY 2010
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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.