Ion Heating

Presented byGennady Fiksel, UW-Madison

for CMSO review panelMay 1-2, 2006, Madison

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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 Ti 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.

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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 functionin solar coronaE. Marsch et al, NPG, 10, 2003

100 km/s ≈ 100 eV for H

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Heavier ions are hotter

From: Cranmer et al., ApJ, 511, 481 (1998)

TO/TO 10

Hydrogen Oxygen

TO > TH

Strong perpendicular heating of oxygen

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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.

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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.

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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.

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Magnetic energy is released

Reconnection EventsExplosive growth ofmagnetic fluctuations

MST Experiment

MST - Ion heating during reconnections

Impurities (C5+)

Majority ions

Ions are heatedTC >> TD during reconnection. Agrees with observations in solar corona.TC ≈ TD away from crash.

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Co- low magnetic fluctuationsCounter- high magnetic fluctuations

Merging spheromaksCo-helicity orCounter helicity

Co- no ion heatingCounter- strong ion heatingElectron temperature the same

magnetic fluctuations

ion and electron heating

MRX - strong ion heating during counter-helicity spheromak merging

Courtesy of H. Ji

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Bi- and unidirectional flows in the lab and the Sun

SSX M. Brown

V (km/sec)

0 20 40 60-20-40-60

Unidirectional

Bi-directional

Courtesy of M. Brown

Sun (SOHO)Innes, Nature, 1997Innes, Solar Physics, 1997

?

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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.

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Example of multiple reconnections -edge modes removed - no ion heating

Edge modes

Core modes

Magnetic energy

Ion temperature

Edge modes removed

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Theoretical approach

• Theory studies of ion heating have been concentrated on tearing modes induced ion flows and their viscous damping.

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Flow flowchart

Sheared flow Compressible flow

Cross-field flow

Uniform electric

field

Compressible flow

Sheared flow

Parallel flow

Kinetic simulations

e/i/Z componentplasma

EstimatesBraginski

Dielectric tensor withcollisional

corrections.Weak

collisionality

Kinetic computations

exact collisionaloperator.Arbitrary

collisionality.

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Sheared flow Compressible flow

Cross-field flow

Flow chart

Dielectric tensor withcollisional

corrections.Weak

collisionality

Kinetic computations

exact collisionaloperator.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 Ti.

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Flow chart

• Strong E|| observed in experiment

• Electrons drag impurities which are heated through collisions with bulk ions.

• Strong electron and impurity flows (vflowvthermal) required for heating.

Uniform electric

field

Compressible flow

Sheared flow

Parallel flow

Kinetic simulations

e/i/Z componentplasma

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• 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.

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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.

The End