1. Ion Heating Presented by Gennady Fiksel, UW-Madison for CMSO review panel May 1-2, 2006, Madison

2. CMSO Scope of the problem In many laboratory and space plasmas the ions are hotter than expected (e.g. in Reversed Field Pinch ions are hotter than expected from collisional e/i heating). Frequently the ions heating exhibits explosive behavior with a strong temperature increase in a short time. Examples: Hot ions in solar corona. High T i and fast ion heating in reconnection experiments and RFP. The phenomenon is very robust and well documented. At the same time it is poorly understood.

3. CMSO Ions are hot in solar corona Spectroscopic measurements indicate the ions in solar corona (r > 1.5R ) are very hot. Indications that the ions are especially hot in polar corona holes, where the electrons are relatively cold. Heavier ions are hotter than protons. Anisotropic velocity distribution function Ion velocity distribution function in solar corona E. Marsch et al, NPG, 10, 2003 100 km/s 100 eV for H

4. CMSO Heavier ions are hotter From: Cranmer et al., ApJ, 511, 481 (1998) T O /T O 10 HydrogenOxygen T O > T H Strong perpendicular heating of oxygen

5. CMSO Plan of action Different mechanisms proposed for solar ion heating Focus first on laboratory work. Understand, within the framework of the Center, the connection of ion heating and magnetic self- organization. Expand our understanding to extra-terrestrial plasma.

6. CMSO Some features of laboratory ion heating Anomalously high ion temperature observed in Reversed Field Pinches, spherical tokamaks, merging spheromaks. Energy source - magnetic field energy released during reconnections. Large fraction of the energy is deposited either in the form of ion thermal energy or ion flows. Different heating for light majority ions and heavy minority ions.

7. CMSO Diagnostics Active and passive ion Doppler spectroscopy for minority ions Rutherford scattering diagnostic for majority ions Diagnostic neutral beams Probes (current, magnetic, optical) Good spatial and temporal resolution. The Center diagnostics: sophisticated, often unique, up to the challenging measurements.

8. CMSO Magnetic energy is released Reconnection Events Explosive growth of magnetic fluctuations MST Experiment MST - Ion heating during reconnections Impurities (C 5+ ) Majority ions Ions are heated T C >> T D during reconnection. Agrees with observations in solar corona. T C T D away from crash.

9. CMSO Co- low magnetic fluctuations Counter- high magnetic fluctuations Merging spheromaks Co-helicity or Counter helicity Co- no ion heating Counter- strong ion heating Electron temperature the same magnetic fluctuations ion and electron heating MRX - strong ion heating during counter-helicity spheromak merging Courtesy of H. Ji

10. CMSO Bi- and unidirectional flows in the lab and the Sun SSX M. Brown V (km/sec) 0204060-20-40-60 Unidirectional Bi-directional Courtesy of M. Brown Sun (SOHO) Innes, Nature, 1997 Innes, Solar Physics, 1997 ?

11. CMSO Ion heating and tearing fluctuations Magnetic reconnections in MST are caused by rapid growth and non-linear interaction of tearing modes. How to relate it to ion heating? Challenge: – Rapid growth of T requires high power 10 MW – The heating depends not only on the mode amplitude but also on their spatial localization and non-linear interaction.

12. CMSO Example of multiple reconnections - edge modes removed - no ion heating Edge modes Core modes Magnetic energy Ion temperature Edge modes removed

13. CMSO Theoretical approach Theory studies of ion heating have been concentrated on tearing modes induced ion flows and their viscous damping.

14. CMSO Flow flowchart Sheared flowCompressible flow Cross-field flow Uniform electric field Compressible flow Sheared flow Parallel flow Kinetic simulations e/i/Z component plasma Estimates Braginski Dielectric tensor with collisional corrections. Weak collisionality Kinetic computations exact collisional operator. Arbitrary collisionality.

15. CMSO Sheared flowCompressible flow Cross-field flow Flow chart Dielectric tensor with collisional corrections. Weak collisionality Kinetic computations exact collisional operator. Arbitrary collisionality. Heating stronger for impurities Heating rate is consistent with experiment IF : – flow thermal speed – scale ion gyroradius Strong ion flows have been observed in SSX. Have not been observed in MST. However, if the spatial and temporal resolution is not sufficient such flows can be misinterpreted as high T i.

16. CMSO Flow chart Strong E || observed in experiment Electrons drag impurities which are heated through collisions with bulk ions. Strong electron and impurity flows (v flow v thermal ) required for heating. Uniform electric field Compressible flow Sheared flow Parallel flow Kinetic simulations e/i/Z component plasma

17. CMSO Interplay of ion heating and core/edge modes Collisional dissipation of parallel flows – parallel and perpendicular gradients – large parallel viscosity – neoclassical effects Future plans - theory Kinetic treatment. Nonlinear resistive MHD modeling. Nonlinear two fluid computations with NIMROD.

18. CMSO Future plans - experiment New diagnostics and improved resolution measurements – upgrade of CHERS diagnostic neutral beam – new Mach probe - ion heating from flow dissipation – new optical probe - local Doppler spectroscopy Dependence of ion heating on Z/M – compare to theory – identification of the heating mechanism – compare to solar- and space plasma. Ion heating and tearing modes. Joint measurements and shared diagnostics on MST, MRX, and SSX.

19. The End