Transcript PPTX

D.J. Den Hartog, R. M. Magee, S.T.A. Kumar, V.V. Mirnov
(University of Wisconsin–Madison)
D. Craig (Wheaton College)
G. Fiksel (Laboratory for Laser Energetics)
J.B. Titus (Florida A&M University)
MMFW
Madison, Wisconsin
6 May 2011
Ions are heated impulsively during magnetic
reconnection.
• Energy is transferred from the
equilibrium magnetic field to ion
thermal energy.
• Heating time (100 μs) is much
faster than i-e collision time (10 ms).
• Power flow from equilibrium
magnetic field is larger than Ohmic
input power.
Pmag ~ 10 kJ/ 100s = 100 MW
Pohmic ~ 5 MW
Outline
•
Magnetic reconnection in MST
•
Majority ion energy distribution
– Neutron flux measurements
– Neutral particle energy spectra
Small population of fast ions generated during reconnection
•
Impurity ion temperature
– CHERS measurements of local C+6 Tperp and Tpar
Anisotropy with Tperp > Tpar during heating
The Madison Symmetric Torus is a large,
moderate current reversed field pinch.
R = 1.5 m
Ip ~ 400 kA
ne = 0.4 - 2.0 x 1019 m-3
a = 0.52 m
B = 0.5 T
Ti,e = 0.2 - 2 keV
Magnetic reconnection in MST is impulsive
and periodic.
• Reconnection events are characterized by a burst of resistive tearing
mode activity.
Much is known about ion heating in MST.
• Equilibrium magnetic field is the ultimate energy source.
• The heating rate is very large (3-10 MeV/s).
• The majority ion heating efficiency ~ m1/2.
• Fully-developed magnetic turbulence is required (i.e. m=0 is a
necessary condition).
• Impurities tend to be hotter than the majority ions.
However, a comprehensive theoretical model of the
heating mechanism remains elusive.
Measurements of majority ion energy distribution
Neutron flux measurements provide
information about ion energies.
• D-D fusion reaction produces neutrons,
• Neutron emission rate is a
function of ion energy and density,
• A small number of fast ions can produce
as many neutrons as a thermal plasma.
Neutron flux measurements do not agree with
predictions using Maxwellian assumption.
• Measured neutron flux is much larger than expected for thermal ions
Information about fi can be obtained from
neutral flux measurements.
electrostatic
energy analyzer
•The neutral flux is related to fi(v,x) by
• Attenuation (α) and neutral density
profile (na) are known, so information
about fi can be extracted.
D+
D0
electron multiplier
He stripping cell
Derived ion energy spectrum reveals a
significant tail in ion distribution function.
• fi(E) is well-modeled by
fi(E) = A exp(-E/T) + B E-γ
• Spectral index
• varies with density
• decreases rapidly during
reconnection events
after reconnection
before reconnection
Fast ion density 2-6% in low density case,
<1% in high.
Ion acceleration mechanisms
E|| induced during reconnection can
accelerate ions to high energies.
• Characteristics:
• core amplitude ~ 50 V/m
• duration ~ 100 μs
• extends across minor radius to
suppress current in the core and
drive current in the edge
• Ion acceleration from parallel electric
field has been used elsewhere (MAST,
ZETA) to explain suprathermal ion
population.
• Plausible scenario for MST.
(Courtesy of W. Ding.)
Ions bouncing off of moving magnetic mirrors
can gain energy (Fermi acceleration).
• First proposed by Fermi (1949) to
explain high energy cosmic rays.
• Applied to Earth’s magnetosphere to
explain high energy electrons (Drake,
2006).
• Predicts beta dependent power law
energy distribution (γ = 3.7 for β=0.16).
Measurements of impurity ion temperature
CHERS can measure both Tperp and Tpar locally.
• CHarge Exchange Recombination Spectroscopy measures C+6 impurity ion
temperature.
(Courtesy of S. Oliva.)
Impurity ion temperature anisotropy is
observed during reconnection heating.
• Tperp > Tpar during heating implies perpendicular heating mechanism.
• ΔTpar decreases with density, ΔTperp does not.
• Anisotropy increases with density, contrary to expectation from
collisional isotropization.
Energy flows through multiple channels.
energy
energy
Tperp,C
Tperp,D
Tpar,C
Tpar,D
Cranmer et. al. Astrophys. J. 518, (1999)
Inverse density dependence of ΔTpar
reproduced by model with varying Zeff
•Known impurities (C, B, O, N,
Al) included in proportion to
give:
Zeff = 4.2 in low density
Zeff = 2.0 in high density
Summary
• High energy tail appears in majority ion distribution function.
• Generated at reconnection.
• Well-described by power law.
• A few percent of total density, with energy ~ 1 - 5+ keV.
• Ion runaway and Fermi acceleration are possible mechanisms.
• Impurity ion anisotropy appears during heating with Tperp > Tpar.
• Implies perpendicular heating mechanism (ICRH or stochastic
heating).
• Density dependence of anisotropy may be due to changing
relative impurity content.