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Comparing classical and lab plasma dynamos S. Prager University of Wisconsin useful discussions with D. Craig, H. Ji, J. Sarff, E. Zweibel • The classical dynamo well-posed problem(s) • The lab plasma dynamo well-posed • The astrophysical field generation problem maybe less clear The classical dynamo problem velocity-driven V energy source ˜v B˜ fluctuations (with seed B) B mean, large-scale Poynting flux Poynting flux is outward from plasma volume P V d dt B 2 20 dV E B dS <0 j E dV > 0, source term j 2 dV j v˜ B˜ dV >0 Magnetic helicity flux Magnetic helicity flux direction is unclear dHm B dS dt E B dV J B dV using Ohm’s law dHm B dS dt > 0 in all lab cases < 0 in sodium expts < 0 in Taylor state unclear in astrophysics The classical dynamo P V Hm or P V Hm The lab plasma dynamo Magnetically-driven B energy source ˜v B˜ fluctuations B mean, large-scale two cases: •Free relaxation (no energy or helicity injected) •Driven relaxation (energy and helicity injected) Free relaxation Poynting flux = 0 = helicity injection large-scale field, <B>, transported by fluctuations ( v˜ B˜ in MHD) 200 magnetic energy (kJ) Helicity (Wb) 150 100 50 0 0.08 0.06 0.04 0.02 0.00 -3 -2 -1 0 1 Time (ms, relative to crash) Time (ms) 2 3 Driven relaxation Poynting flux 0 helicity injection Hm P Magnetic field grows and redistributes Experimental examples in a torus (e.g. reversed field pinch) dHm ˜ torV˜tor 2 E˜ B˜ dV dt helicity injection through surface E˜ pol ( 0 ) E˜ tor ( 0 ) ˜ tor V˜tor ˜ pol EÝ = toroidal flux ~ = toroidal loop voltage ~ E˜ tor dc injection of helicity fluctuations v(,k) B(,k) B experimental result MST McCollam, Blair, Sarff another experimental example dHm dt (B dS) spheromak E˜ B˜ dV One physics link between the classical and lab dynamos ˜ can be driven by instability In both cases, v˜ B or nonlinear coupling lab dynamo shows alpha effect can be large, that dynamo quenching predictions are not Indicates universal The astrophysical field generation problem B fields are observed or deduced to •Grow from a seed field (Earth, ISM…) •Oscillate in time (Earth, Sun….) •Be transported in spatial scale or wavenumber (ISM….) •Be transported through space (Extragalactic jets…) Lab relaxation processes can contribute to the latter three What are the most important problems in the generation of magnetic fields in astrophysics? Coupling of two dynamo processes e.g., discussed by Blackman velocity-driven dynamo P Hm magnetic-driven dynamo (relaxation) velocity-driven dynamo on LHS drives relaxation or field growth on RHS Coupling of two dynamo processes e.g., discussed by Blackman velocity-driven dynamo Hm P Hm magnetic-driven dynamo (relaxation) velocity-driven dynamo on LHS drives relaxation or field growth on RHS Solar fields P V dynamo Disk/Jet/lobe system disk engine velocity-driven dynamo Jet/lobe P magnetic-driven dynamo (relaxation) Disk/Jet/lobe system P Jet/lobe magnetic-driven dynamo relaxation, transport of B over over space, transport of B from high to low k Magnetic energy in the universe other 1 2 jets/lobes Magnetic energy in the universe other is this correct? 1 2 jets/lobes so, magnetic transport and consequent creation of largescale field may be important (the lab plasma dynamo or magnetic dynamo) Summary Two B generation mechanisms can work together velocity-driven engine (dynamo) internal energy source in flow contains little magnetic energy (?) occupies small space (?) magnetically-driven relaxation driven by boundary condition produces large-scale field via transport contains large magnetic energy (?) occupies large space (?) Summary Two B generation mechanisms can work together velocity-driven engine (dynamo) internal energy source in flow contains little magnetic energy (?) occupies small space (?) magnetically-driven relaxation driven by boundary condition produces large-scale field via transport contains large magnetic energy (?) occupies large space (?) Should the astrophysical “dynamo problem” be broadened to include both effects about equally?
