Non-Classical Electron Energization Associated
with Tearing Mode Reconnection in MST
Plasmas
Ami M. DuBois
A.F. Almagri, J.K. Anderson, D.J. Den Hartog, C. Forest, M.D. Nornberg,
and J.S. Sarff
EPR Workshop
●
Auburn, AL
●
23 - 26 February 2016
Particle heating and energization are observed in
space plasmas and in laboratory experiments
• Particle heating and energization during magnetic
reconnection have been observed in:
• Solar flares
• Magnetosphere (magnetotail, substorms)
• Laboratory
• Mechanisms responsible are still not fully understood
The Madison Symmetric Torus (MST) provides an opportunity to
study heating and energization processes in a laboratory
setting.
Energization due to classical mechanisms is observed
in laboratory experiments such as tokamaks
• In tokamak experiments, electron
energization observed during
sawtooth crashes
• Generation of non-thermal
electrons attributed to electron
runaway due to induced parallel
electric fields (classical mechanism)
A. Fasoli, et al. Nucl. Fusion, 48, 034001 (2008)
Energy (keV)
X-ray Flux (counts/keV/s)
Will show the first experimental measurements of nonclassical energization during magnetic reconnection
Time relative to reconnection event (ms)
Outline
• The Madison Symmetric Torus & tearing mode reconnection
• Ion heating & energization
• Electron energization
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–
–
–
Fast x-ray detector
Initial measurements
Energization energy source
Electron runaway acceleration
• Summary
The Madison Symmetric Torus (MST) reversed field
pinch (RFP)
• In the RFP, the magnetic field is generated by induced plasma current.
• Plasma is ohmically heated by plasma current.
•
•
•
•
•
•
•
R/a = 1.5 m / 0.5 m
Ip < 0.6 MA
B ≤ 0.6 T
Te > 200 eV
Ti < 2 keV
ne ~ 1019 m-3
τpulse < 0.1 s
Standard RFP plasmas are subject to tearing mode
instabilities and magnetic reconnection events
Reversal surface location
can be adjusted or
removed (𝐹𝐹 = 𝐵𝐵𝑡𝑡 𝑎𝑎 / 𝐵𝐵𝑡𝑡 )
Tearing instabilities and nonlinear coupling results in multiple magnetic
reconnection sites
Ion heating & energization
Release of magnetic energy results in ion heating
• Energy stored in equilibrium magnetic
field suddenly drops (20 kJ released)
• Large fraction of magnetic energy is
transferred to ions
𝑇𝑇𝑖𝑖⊥
• Heating mechanism is non-collisional
– Heating time ~ 100 μs
– i-e collision time ~ 10 ms
– 𝑇𝑇𝑖𝑖 ≫ 𝑇𝑇𝑒𝑒
Ion heating is anisotropic and species dependent
• Minority ions:
– Hotter than majority ions
– Heated more strongly in direction perpendicular to B
• Heating is dependent on charge & mass for all ions
S. Gangadhara et al, PoP, 15, 056121 (2008)
R. Magee et al, PRL, 107, 065005 (2011)
High energy tail develops in majority ion energy
distribution
𝑓𝑓𝐷𝐷+ 𝐸𝐸 = 𝐴𝐴𝑒𝑒 −𝐸𝐸/𝑘𝑘𝑘𝑘 + 𝐵𝐵𝐸𝐸 −𝛾𝛾
• Ion spectrum well-fit by Maxwellian
plus power-law tail
• Tail spectral index:
High n
Low n
– Indicates production of tail distribution
– Decreases rapidly during reconnection
events
– Varies with density
• Possible mechanisms:
– Ion runaway [S. Eilerman et al, PoP 22, 020702 (2015)]
R. Magee et al, PRL, 107, 065005 (2011)
Ion heating is diminished when coupling between
core and edge tearing modes is weak
Non-linear coupling of m = 0 mode is a key ingredient for:
Ion heating is diminished when coupling between
core and edge tearing modes is weak
Non-linear coupling of m = 0 mode is a key ingredient for:
1) Release of magnetic energy
Ion heating is diminished when coupling between
core and edge tearing modes is weak
1) Release of magnetic energy
Non-linear coupling of m = 0 mode is a key ingredient for: 2) Generation of dynamo
Ion heating is diminished when coupling between
core and edge tearing modes is weak
1) Release of magnetic energy
Non-linear coupling of m = 0 mode is a key ingredient for: 2) Generation of dynamo
3) Perpendicular ion heating
Electron Energization
Thomson Scattering measures decrease in thermal
electron temperature
• Bulk electron distribution is cooled during
reconnection.
• Flattening of Te(r) profile provides evidence
for enhanced electron heat transport.
Why is ion heating and energization measured, but
observe cooling of electrons?
• Cooling of bulk electrons is probably the result of increased
stochastic thermal transport.
• This may mask electron energization during reconnection events.
• Energetic electrons expected to be lost faster than thermal
electrons.
• Therefore, sensitive high-speed measurements of the electron
energy distribution are required to uncover possible reconnection
effects.
–
–
–
–
Avalanche photodiode
20 ns Gaussian shaping amp
500 MHz digitization
3 – 25 keV optimal sensitivity
• Fast shaping time enables dynamics of
energetic electron generation and losses
during reconnection events to be
uncovered.
A.M. DuBois et al, RSI 86, 073512 (2015)
Time (ms)
Energy (keV)
• High time resolution soft x-ray detector
Amplitude (V)
The fast x-ray detector has a 20 ns response time
Time (ns)
In
Bp
Bt
•
•
•
Out •
Ip = 500 kA
F = -0.2
ne = 0.8x1019 m-3
Radial view through
core
• X-ray flux shows an increase in energetic
electrons at reconnection event, similar to
measurements of energetic ion tail.
X-ray Flux (counts/keV/s)
FXR
Energy (keV)
High energy x-ray flux is enhanced during reconnection,
but energetic electrons are lost rapidly
Time relative to reconnection event (ms)
• Fast decay of high energy x-ray flux indicates energetic electrons are lost faster
than ions, consistent with stochastic transport.
In
Bp
Bt
•
•
•
Out •
Ip = 500 kA
F = -0.2
ne = 0.8x1019 m-3
Radial view through
core
• X-ray flux shows an increase in energetic
electrons at reconnection event, similar to
measurements of energetic ion tail.
X-ray Flux (counts/keV/s)
FXR
Energy (keV)
High energy x-ray flux is enhanced during reconnection,
but energetic electrons are lost rapidly
Time relative to reconnection event (ms)
• Fast decay of high energy x-ray flux indicates energetic electrons are lost faster
than ions, consistent with stochastic transport.
Fast x-ray measurements reveal the formation of
energetic tail during reconnection
• Energetic tail best described by power-law
– Tail spectral index (γ) is measure of degree of energetic tail that is generated
– γ decreases rapidly from 4.14 to 1.81 (Δγ = 2.33)
Energy (keV)
Change in magnetic
energy (kJ)
Γ 𝐸𝐸 = B𝐸𝐸 −𝛾𝛾
Tail spectral index
Flux (ergs/s/keV)
• May indicate a similar mechanism as ion heating/energization
Time (ms)
Energization energy source
The released energy from the equilibrium magnetic
field is the source for energetic electrons
• Varied plasma parameters to change amount of magnetic energy released
from equilibrium magnetic field
• Δγ increases asymptotically as a
function of amount of released
magnetic energy
• More magnetic energy released results
in electrons gaining energy,
enhancement of energetic tail
Δ𝛾𝛾 = 𝛾𝛾𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 − 𝛾𝛾𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑
• Δγ measures how much of energetic tail is generated during reconnection
compared to before event (independent of plasma parameters)
Released magnetic energy (kJ)
Coupling between edge and core modes is essential
for electron energization as it is for ion heating
• m = 0 tearing modes facilitate core to edge communication
— Weak coupling when m = 0 tearing resonance removed from plasma (F = 0)
— Strong coupling when tearing resonance in plasma (F = -0.3)
F = -0.3
F = -0.2
F=0
Flux: E ≥ 15 keV
m = 0, n = 1
amplitude (G)
• High energy x-ray flux greatly diminished when m = 0 mode activity reduced
• Δγ also decreases for weak coupling
Time (ms)
Δγ = 3.39
Δγ = 2.33
Δγ = 1.07
F = -0.3
F = -0.2
F=0
Time (ms)
Classical electron runaway acceleration
The high energy x-ray flux is significantly decreased
looking along Bt compared to perpendicular direction
• Expect anisotropy in angular
distribution of bremsstrahlung
emission (modeling underway)
Time (ms)
Gap
Top
View
Bp Bt
X-ray flux (counts/keV/s)
– 𝐸𝐸∥ < 100 𝑉𝑉/𝑚𝑚
– Could accelerate electrons to MeV
Energy (keV)
• Energization mechanism plays important role in
converting released magnetic energy into
particle energization
• Electron runaway initially expected to be more
prominent:
FXR
Tail spectral index
Measured x-ray flux normalized
to account for difference in
plasma volume viewed and
number of events per dataset
∆𝜸𝜸 = 𝟐𝟐. 𝟐𝟐𝟐𝟐 ± 𝟎𝟎. 𝟏𝟏𝟏𝟏
∆𝜸𝜸 = 𝟐𝟐. 𝟑𝟑𝟑𝟑 ± 𝟎𝟎. 𝟎𝟎𝟎𝟎
Perpendicular
Parallel
Time (ms)
Flux (ergs/keV/s/str/cm^3)
A more substantial energetic tail is generated perpendicular
to the core magnetic field than in the parallel direction
0.5 ms before
Perpendicular
Parallel
during
Perpendicular
Parallel
Energy (keV)
∆𝛾𝛾 indicates electrons may be strongly
energized perpendicular to B – similar to
ion heating
The parallel electric field does not appear to be a
mechanism in the energization process
Ip (kA)
ne (x1019 m-3)
F
500
0.8
-0.2
500
0.8
0
500
0.5
-0.2
500
1.2
-0.2
400
0.8
-0.2
400
0.8
-0.1
300
0.8
-0.4
500
0.8
-0.3
Δ𝛾𝛾 = 𝛾𝛾𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 − 𝛾𝛾𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑
• In previous experiments, injected fast ions gained energy at reconnection events,
consistent with runaway acceleration mechanism
• If electron runaway was responsible for the observed electron energization,
Δ𝛾𝛾 expected to increase with 𝐸𝐸∥
Parallel Electric Field (V/m)
Summary
• Reconnection events in MST characterized by bursts of tearing
mode activity
• Non-collisional ion heating/energization observed at reconnection
events, but thermal electrons are cooled
• Non-classical electron energization observed during reconnection
events:
– Enhancement of energetic tail greatest for largest amount of energy released from
equilibrium magnetic field
– Coupling between edge & core tearing modes essential for energization
– Measurements reveal electrons are energized more strongly in direction
perpendicular to B (modeling underway to confirm emission anisotropy)
– No clear dependence of tail generation on E// (runaway acceleration)
This material is based upon work supported by the U.S. Department of Energy, Office of Fusion Energy Sciences under award
number DE-FC02-05ER54814 and the National Science Foundation.