Plasmas in Laboratory and Astrophysics Plasmas in Laboratory and Astrophysics Alfven Wave Turbulence and Alfven Wave Turbulence and Heating. Heating. Center for Multi-scale Plasma Dynamics. Center for Multi-scale Plasma Dynamics. Bill Dorland, Maryland. Bill Dorland, Maryland. Alex Schekochihin, Cambridge. Alex Schekochihin, Cambridge. Steve Cowley, UCLA/Imperial College. Steve Cowley, UCLA/Imperial College. Troy Carter, Brian Brugman,Warren Lyberger, Pat Pribyl, Troy Carter, Brian Brugman,Warren Lyberger, Pat Pribyl, UCLA. UCLA. Greg Howes, Eliot Quataert, Berkeley. Greg Howes, Eliot Quataert, Berkeley. Greg Hammett, Princeton. Greg Hammett, Princeton. Thanks to: Stewart Prager, U. Wisconsin and the members Thanks to: Stewart Prager, U. Wisconsin and the members of the of the Center for Magnetic Self Organization Center for Magnetic Self Organization for data. for data.
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Plasmas in Laboratory and Astrophysics Alfven Wave Turbulence and Heating. Center for Multi-scale Plasma Dynamics. Bill Dorland, Maryland. Alex Schekochihin,
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Plasmas in Laboratory and AstrophysicsPlasmas in Laboratory and AstrophysicsAlfven Wave Turbulence and Heating.Alfven Wave Turbulence and Heating.
Center for Multi-scale Plasma Dynamics.Center for Multi-scale Plasma Dynamics.Bill Dorland, Maryland.Bill Dorland, Maryland.Alex Schekochihin, Cambridge.Alex Schekochihin, Cambridge.Steve Cowley, UCLA/Imperial College.Steve Cowley, UCLA/Imperial College.Troy Carter, Brian Brugman,Warren Lyberger, Pat Pribyl, UCLA.Troy Carter, Brian Brugman,Warren Lyberger, Pat Pribyl, UCLA.Greg Howes, Eliot Quataert, Berkeley.Greg Howes, Eliot Quataert, Berkeley.Greg Hammett, Princeton.Greg Hammett, Princeton.Thanks to: Stewart Prager, U. Wisconsin and the members of theThanks to: Stewart Prager, U. Wisconsin and the members of theCenter for Magnetic Self Organization Center for Magnetic Self Organization for data.for data.
Accretion and MHD.Accretion and MHD.
Instability Tangled BField.
Momentum transport.
Gravitational energy loss
Turbulent energy
Dissipation, Heat to ??• Electrons -- radiation.• Ions -- swallowed by black hole.Quataert and Gruzinov.
Magnetic self-organization in the lab., MST Magnetic self-organization in the lab., MST Reversed Field Pinch at Wisconsin, Reversed Field Pinch at Wisconsin, Prager Prager et. al.et. al.
–2–1012Time (ms)1.50.50 Q
(MW/m2)
30200 V
(km/s)
100.40.20 Tion
(KeV)
C4+.07.06Φ/πa2
( )T
.04.020 bB(a)
~1.0
€
˜ B
B
toroidal magnetic flux
heat flux(MW/m2)
rotation(km/s)
ion temperature(keV)
dynamo
magnetic fluctuations
energy transport
momentum transport
ion heating
time (ms)
Small Scales.Small Scales.
Kraichnan argued that the small scale motions will see a large quasi-uniform field. The small scale motions will become Alfven/slow waves traveling along a roughly uniform B.
Most of the dissipation happens at small scales -- thesearguments suggest that the dissipation is of small amplitude Alfven/slow waves.
Introduction.Introduction.
• Need to understand the turbulent cascade of Alfven waves.Need to understand the turbulent cascade of Alfven waves.
Many applications: astrophysics, fusion, space.Many applications: astrophysics, fusion, space.
Numerically it is hard to compute the heating this way because energy sloshes in and out of particles. We canshow that it is equivalent to an expression derived from ENTROPY PRODUCTION.
This term is positive and much easier to average, heating always comes from collisions even in collisionless regime!
Mixing in Phase Space.Mixing in Phase Space.
• f(f(r,vr,v,t) is conserved along particle orbits in ,t) is conserved along particle orbits in collisionless motion. collisionless motion.
• Stochasticity in orbits leads to fine scale mixing - Stochasticity in orbits leads to fine scale mixing - jagged f. Less collisions jagged f. Less collisions more jagged f. more jagged f. Entropy production becomes independent of Entropy production becomes independent of collision rate. collision rate.
f
v
New SimulationsNew Simulations
• Current simulations are doing the kinetic Current simulations are doing the kinetic regime and caculating the ion and electron regime and caculating the ion and electron heating. heating. QQee=Q=Qee(T(Tee/T/Tii, , ), Q), Qii=Q=Qii(T(Tee/T/Tii, , ) ) Bill Bill
Dorland, Greg Howes.Dorland, Greg Howes.
• Need to understand the cascade in this Need to understand the cascade in this regime and examine the dynamics.regime and examine the dynamics.
• Single Pass Design.Single Pass Design.• Alfvén waves are Alfvén waves are
launched into the open launched into the open plasma column.plasma column.
• Only co-propagating Only co-propagating geometry is possible.geometry is possible.
• Reflecting Cavity DesignReflecting Cavity Design• Alfvén waves are Alfvén waves are
launched into a plasma launched into a plasma column terminated by a column terminated by a reflecting platereflecting plate
• Co- and Counter-Co- and Counter-propagating interactions propagating interactions occuroccur
• Using the Using the Natural MASERNatural MASER as the pump wave and the as the pump wave and the Driven Driven MASERMASER as a sideband the as a sideband the dependence of the instability dependence of the instability may be investigated.may be investigated.
The Spontaneous and Driven cavity waves The Spontaneous and Driven cavity waves in Concert are also Unstablein Concert are also Unstable
Possible Experiment GeometriesPossible Experiment Geometries
• Single Pass, co-propagating and Single Pass, co-propagating and counter-propagating separatelycounter-propagating separately
Multiple pass, co-propagating and Multiple pass, co-propagating and counter-propagating combinedcounter-propagating combined
CONCLUSIONSCONCLUSIONS
• Well defined problem that needs a solution.Well defined problem that needs a solution.
• Excellent use of fusion codes - well adapted Excellent use of fusion codes - well adapted to the problem.to the problem.
• Experimental study on LAPD will yield Experimental study on LAPD will yield further results this year.further results this year.