Where'does'the'energy'
come'from,'what'form'does'
it'take,'and'how'is'it'
dissipated?'
The&solar&photosphere&is&at&
~&5800K&and&the&corona&is&at&
~&106K&
Statement'of'the'problem:'
1&
Coronal&hea(ng&
1&
XLrays&(~3MK)&from&Yohkoh&SXT&(JAXA/NASA/STFC)&
STFC&Advanced&School,&Warwick&2012&
Lyndsay'Fletcher'
School&of&Physics&and&Astronomy,&SUPA&
University&of&Glasgow&
Solar&ac(vity:&
Coronal&Hea(ng&&
and&&
Solar&Flares&
•  Magne(c&stresses&dissipated&in&the&solar&corona&
•  Magne(c&free&energy&fed&in&from&the&lower&layers&
•  Same&basic&problem&–&how&to&&
&&&&&convert&magne(c&free&energy&&
&&&&&into&other&forms&(difficult&in&a&
&&&&&highlyLconduc(ng&plasma)&
•  Some&coronal&hea(ng&ideas&&
&&&&&propose&a&mul(tude&of&small&&
&&&&&flares&
What'do'they'have'in'common?'
Coronal&hea(ng&and&solar&flares&
NB,&the&flare&is&the&increase&in&
radia(on.&The&associated&mass&
mo(on&is&the&coronal&mass&ejec(on&
Where'does'the'energy'to'
heat'the'corona'come'from,'
what'form'does'it'take,'and'
how'is'it'dissipated?'
A&region&of&the&Sun&
suddenly&brightens,&heats&
and&produces&copious&
accelerated&par(cles.&
Statement'of'the'problem:'
Solar&flares&
&ver(cal&T&structure&&
In&fact,&because&of&its&greater&mass,&
the&energy&requirement&is&greater.&
The&hea(ng&problem&really&begins&in&
the&chromosphere.&&
Coronal&hea(ng:&&
L&QuasiLsteady&hot&corona&means&a&
quasiLcon(nuous&dissipa(on&process&
L &No&need&for&coronal&energy&storage&
L &Plasma&remains&almost&Maxwellian&
Chromospheric&hea(ng&
Flares:&
L&Rapid&character&of&flare&means&very&
intermicent&energy&dissipa(on&
L &Need&for&longLterm&energy&storage.&&&
L &Plasma&becomes&nonLMaxwellian&&
•  Coronal&hea(ng&is&quasiLsteady:&on&observa(onal&(mescales&
the&plasma&evolves&slowly&&
•  Flares&are&abrupt:&plasma&heats&and&evolves&rapidly&
•  &A&further&significant&difference&L&flares&involve&large&numbers&
of&nonLthermal&electrons&which&are&not&detected&in&the&nonL
flaring&hot&corona&
What'is'different?'
Coronal&hea(ng&and&solar&flares&
The&corona&
7&
Composite&white&light&corona&and&UV&image&of&the&chromosphere&
β&<&1&out&to&~&2R&&(magne(c&forces&dominate)&
(Electrons)'
(Dust)'
The&‘white&light’&corona&is&formed&by&Thomson&scacering&of&photospheric&light&by&
free&electrons&in&the&coronal&magne(c&field.&
For&h&>&2300&km,&radiated&
energy&can&no&longer&&
compete&with&the&rate&of&&
energy&input&so&the&&
temperature&rises&rapidly&
&The&height&ranges&of&&
&forma(on&of&the&principal&
&emission&lines&are&shown&
&Plot&of&Temperature&vs&
&height&above&the&&
&photosphere&
Chromosphere&&&corona&
EUV&and&XLray&corona&
Red,&green&and&white&light&corona&during&an&
eclipse.&Habbal&et&al.&(2010)&
9&
T&~&1MK.&EUV&emission&is&line&
emission&from&highly&ionised&Fe&
(principal&radia(ng&coolant)&
NASA/TRACE&
T&~&3L5MK.&Most&XLray&emission&is&
freeLfree&(bremsstrahlung)&from&
hot,&quasiLthermal&plasma&
NASA/ISAS/JAXA/Hinode&XRT&
From&space,&we&have&ample&evidence&of&the&millionLdegree&corona&
Fe&X&(red)&line&also&iden(fied&
Its&iden(fica(on&as&a&
forbidden&line&of&&Fe'XIV'
established&the&existence&of&a&
high&Te&corona&
(Gotrian&1939,&Edlén&1942)&&
This&did&not&correspond&to&any&of&the&atomic&transi(ons&expected&at&photospheric&
temperatures.&
The&first&hint&that&the&corona&is&a&bit&strange&came&from&eclipse&observa(ons&of&the&
coronal&‘green&line’&(Harkness&&&Young&1869)&
The&hot&corona&
Observa(onal&problems&are&very&basic.&e.g.&How&
do&you&isolate&and&measure&intensity&in&a&loop?&
Temperature,&density,&emission&measure&
(deduced'from'diagnosAcs)'
Intensity,&doppler&shir,&line&width'(directly'from'
observaAon)'
The&observables&are:&
Each&loop&is&its&own&miniLatmosphere,&thermally&
isolated&from&neighbours.&
The&hot&corona&is&mostly&confined&in&closed&
magne(c&loops&–&the&basic&structural&element&
for&the&corona.&
Coronal&hea(ng&=&loop&hea(ng&
Coronal&loops&
The&problem&is&understanding&
energy&transport&and&dissipaAon.&
No&problem&with&energy&source&L&
there&is&≥&107&erg&cmL2&in&turbulent&
&&wave&energy&at&photosphere…&
Requirement&is&~&106&erg&cmL2&&
The&chromosphere&and&the&
corona&are&heated&by&something&
other&than&conduc(on,&convec(on&
or&radia(on.&
Energy&budget&
T&range&from&Log&T&=&
6.3&L&6.6&
Temperatures&
obtained&from&
Hinode&XRT&filter&
ra(os&show&
temperature&
gradients&and&fine&
structuring&(Reale&
et&al&2007)&
More&about&temperature&
Temperature&
See'‘Living'Reviews'
in'Solar'Physics’'
arAcle'by'Reale'
(2010)'
d(EM(T))&=&ne(T)2&dL&
Possibly&the&most&complete&
picture&of&temperate&comes&
from&emission&measure&
analysis&(e.g.&Warren&et&al&
2011)&
Temperature&measurements&are&very&difficult:&
L &Inconsistent&results&from&photometry&(i.e.&filter&ra(os)&and&spectroscopy&
L &Considerably&differences&depending&how&background&is&subtracted&
Note:&there&are&2&relevant&temperatures,&which&could&be&different.&
• &&&electron&temperature&(determined&from&collisionally&excited&lines,&or&
bremsstrahlung)&&&
• &&&ion&temperature&(from&line&widths).&
Most&modeling&assumes&these&are&the&same&–&single&fluid.&Though&see&work&by&
Bradshaw&&&collaborators&
Intensity&
• &Only&a&small&frac(on&of&loops&are&isothermal&(~10%)&
• &Loops&don’t&seem&to&evolve&from&hot&to&warm&to&cool.&&
• &Possibly&three&‘classes’&of&loop;&hot&(~5MK),&warm&(~2MK),&cool&(<1MK),&located&
in&different&parts&of&an&ac(ve&region.&
Observed&loop&proper(es&
See'‘Living'Reviews'
in'Solar'Physics’'
arAcle'by'Reale'
(2010)'
16&
Bradshaw&&&
Cargill&2006&
Single&loop&modeling&
(Aschwanden&et&al&01)&
⇒ &Footpoint&hea(ng?&
Observed&loop&scale&
height&>&hydrosta(c&
scale&height.&
• &&Loops&exist&for&&>>&conduc(ve&or&radia(ve&cooling&(mescales&–&
again&implies&hea(ng&&
• &Intensity&distribu(on&inconsistent&with&hydrosta(c&equilibrium&–&
implying&hea(ng&and&nonLsteady&flows&
• &Basic&scale&of&transverse&field&structuring&is&s(ll&subLresolu(on&
More&loop&proper(es&
•
•
•
Looks&great&but&it’s&so&complicated…&what&do&we&really&learn?&
Take&a&model&for&magnetoconvec(on&and&extend&the&field&into&the&corona&
Use&the&energy&input&from&lower&atmosphere&as&the&coronal&hea(ng&term&
Explicit&forms&for&energy&dissipa(on&(viscous&hea(ng,&Joule&hea(ng)&
‘Ab&ini(o’&models&L&simulate&the&whole&thing…&
B2/L2
B2/L
17&
18&
Ab'iniAo'modeling&
B/L2
B/L
From&observed&parameters,&calculate&coronal&B,&assume&a&density&then&calculate&
heat&input&and&temperature&for&an&en(re&ac(ve&region&using&1D&loop&model&
Some&models&parameterise&the&hea(ng&input&as&simple&func(ons&of&the&ac(ve&
region&loop&parameters&(e.g.&B,&L,&ρ&V...)&
Parameterised&ac(ve&&
region&modeling&
Lundquist et al. 2008
&Upper&chromosphere&and&corona&must&be&heated&by&a&magne7cally'dominated&
mechanism&
• &&Acous(c&flux&in&the&chromosphere&is&&~&
102&–&103&less&than&needed&to&heat&the&
corona.&
• &Waves&trapped&in&lower&chromosphere&
by&steep&soundLspeed&gradient&
• &Problem&–&this&mostly&happens&in&the&
lower&chromsophere&
Basic&idea&–&upwardsLtraveling&acous(c&compressions&moving&into&low&density&
regions&steepen&into&shocks&which&dissipate&&&heat.&
Biermann&(1946)&and&Schwarschild&(1948)&proposed&acous(c&waves&for&hea(ng&the&
chromosphere&and&the&corona&&
Acous(c&Waves&
•&Field&‘tangling’&and&magne(c&reconnec(on&L&&dissipa(on&of&
energy&at&current&sheets.&
•&MagnetoLacous(c&wave&dissipa(on&L&longitudinal&compressional&
waves&will&form&shocks&like&acous(c&waves&
•&Alfvén&waves&L&good&at&transport,&generally&bad&at&dissipa(on&
(low&shear&viscosity&in&the&corona)&
•&Acous(c&waves&L&now&thought&negligible&for&corona,&since&
trapped&in&chromosphere,&although&some&modeLcoupling&with&
MHD&waves&exists.&
Possibili(es&for&energy&transport&to&corona&and&hea(ng&include:&
Coronal&Energy&Transport&and&Hea(ng&
The&occurrence&rate&of&nanoflares&
is&about&0.4&nanoflares&s–1&in&a&hot&
XLray&loop&and&30&sL1&in&an&EUV&
loop&
Nanoflare&energy&is&es(mated&to&
be&1025&erg&for&XLray&loops&and&
1023&erg&for&EUV&loops.&&
Parker&(1998)&
‘tangled’&coronal&
flux&
• &Current&may&dissipate&directly&by&Joule&hea(ng,&or&by&a&chain&of&events&involving&
magne(c&reconnec(on&
• &Current&sheets&form&at&magne(c&interfaces&(where&curl&B&≠&0)&
• Parker&(1972)&L&slow&random&walk&of&flux&&Ldriven&by&photosphere&and&subL
photosphere&L&tangles&coronal&field.&&
Dissipa(on&in&coronal&&
current&sheets&
Energy&flux&in&observed&waves&is&too&low:&at&higher&frequencies&this&is&unknown…&
Slow&magnetoacous(c&waves&are&iden(fied&and&–&being&compressional&–&dissipate&
readily.&&
Alfven&wave&energy&density&is&unknown&(hard&to&observe).&Also,&hard&to&dissipate&
Alfven&waves,&though&this&can&happen&via&resonant&absorp(on,&phase&mixing.&
MacIntosh&et&al&(2011)&
Coronal&plasma&supports&many&wave&modes.&Imaging&and&spectroscopy&detec(ons&
of&slow,&fast&and&Alfven&modes&have&all&been&claimed.&
MHD&waves&
Hannah&et&al.&2008&
(Bareford&et&al&2011)&
Internal&current&sheets&
form&(red)&leading&to&
reconnec(on&and&hea(ng&
Another&idea&is&that&&a&
single&loop&is&driven&(by&
footpoint&twis(ng)&to&
instability&
24&
Loop&instability&and&microflares&
• &Not&clear&that&the&readily&observable&
proper(es&(e.g.&EUV&intensity)&are&very&
good&proxies&for&total&flare&energy.&
• &Big&problems&coun(ng&very&small&
events&near&the&noise&
• &Spectral&index&ranges&from&1.5&to&2.1&
• &Coronal&hea(ng&requires&a&spectral&
index&in&flare&frequency&distribu(on&&
of&>&2&&(Hudson&1991)&
• &Flares&at&1023&erg&have&not&been&
observed.&
Observed&flares&span&a&large&range&in&energies,&from&microflares&(1024&ergs)&&&
to&great&flares&(1032&ergs).&&
Microflares&and&nanoflares&
…&probably&not&
What&do&we&learn?&
• &&Energy&budget&of&waves&is&not&well&pinned&down&
26&
• &nanoflare&modeling&(intermicent&but&quasiLsteady&energy&input&in&mul(ple&
loops)&does&a&good&job&at&explaining&hot&(~5MK)&loops&and&warm&(~2MK)&loops.&
• &Observed&flare&distribu(on&provides&marginal&evidence&for&nanoflares&
• &S(ll&plagued&by&basic&things…how&to&subtract&the&background?&
• &High&conduc(vity&and&rapid&dynamic&response&of&the&coronal&plasma&smears&
out&any&clear&signatures&of&different&input&models&on&(so&far)&observable&
(mescales.&
We’ve&learned&that&this&is&a&surprisingly&difficult&problem.&
Emission&at&30.4nm,&from&singlyLionised&He.&
NASA/SDO/AIA&
The&mul(tude&of&jets&that&on&average&comprise&the&chromosphere&are&known&as&
spicules.&Perhaps&the&energy&contained&in&the&mass&mo(on&of&the&spicules&heats&
the&corona?&&
Hea(ng&by&spicules?&
Blue&&L&25L50&keV&–&(RHESSI)&
Green&–&thermal&(TRACE)&
Fe&XII&and&Fe&XXIV&emission&(TRACE)&
T&~&20&MK&(~2keV)&
Red&L&12L25&keV&(RHESSI)&
Bremsstrahlung&emission:&&&
28&
Solar&flares&
More&relaxed&
field&–&‘flare&
loops’&
eL&
PostL
reconnec(on,&
field&L&shrinking&
and&relaxing&
Unconnected,&
stressed&field&
Gradual
(SXR)
The&first&known&flare&
Impulsive
(HXR)
(i)&flare&UV&increases&ionisa(on&of&ionosphere&
L&Likened&to&the&star&α&Lyrae,&in&
brilliance&and&colour&(bluishLwhite)&
(ii)&CME&arrives,&disturbing&geomagne(c&field&
Magnetometer&disturbances&following&Carrington’s&
Flare&:&
First&recorded&flare&–&white&light&
drawing&by&Carrington&(1859)&
e.g.&The&Carrington&flare&of&1859&L&first&recorded&flare&observa(on,&and&probably&
the&largest.&Had&this&occurred&in&the&modern&era&its&effects&could&have&been&
catstrophic.&
Footpoint&UV/op(cal&emission,&
fast&electrons/ions&(~50%&of&flare&
energy)&
Energy&
flux&
Reconnection
eL&
Flare&basics&
Energe(cs&
flare&
Flare&total&irradiance&&&
(1)&Emin&is&largest&value&of&low&energy&cutoff&compa(ble&with&HXR&spectrum.&&
(2)&Assumes&Ltotal/Lx&=&100&(e.g.&Kretschzmar&2011)&
(2)
(1)
Energy&per&component&in&units&of&log10&E&(ergs)&
Comparable&to&power&inferred&for&nonLthermal&
electrons&from&hard&XLrays.&
Direct&‘Sun&as&a&Star’&measurement&gives&XL
flare&power&~&1029&erg&sL1&&
~ few&x&10&32&ergs&total&
(Woods&et&al&04,&05,&Kretschmar&et&al&2010)&
Total&flare&energy&is&rather&poorly&known&
–  most&of&the&flare&energy&emerges&in&the&UV&to&op(cal&range&
–  Currently,&this&range&is&not&well&observed&
(Can&do&much&becer&for&stellar&flares&which&have&great&op(cal&coverage)&
Energe(cs&
Woods&et&al&2005&
j&=&∇×B/µ&
Coronal&energy&storage&
Temmer&et&al.&(2010)&
Red – HXR
Grey – d2r/dt2
€
€
α&constant&along&field&lines&
So&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&,&&&&&&&meaning&&
(∇ × B) × B = 0
(∇ × B) = α B
Assume&~&steady&state,&with&negligible&gravita(onal&forces&and&pressure&&
gradients&(low&beta&corona).&Then&&
€
ForceLfree&condi(on,&i.&e.&&field&
and&current&are&aligned&
MHD&Force&balance&equa(on&
 

Dv
−∇p + j × B + ρg = ρ
Dt
Twis(ng&the&field&produces&&‘free&energy’&in&the&form&of&current.&
MHD&version&of&Ampère’s&Law&
Yashiro&et&al.&(2007)&
• &Flare&energy&density&>>&CME&energy&
density&
• &Within&instrumental&(me&resolu(on,&CME&
accelera(on&peaks&simultaneously&with&
hard&XLrays&
• &90%&of&GOES&XLflares&have&a&CME.&&
Flares&and&CMEs&
Krucker&et&al.&(2007)&
Energy&storage&
36&
Blue&=&op(cal&
Orange&=&HXR&&
Sun et al
(2012)
Height&=&2Mm&
=&0.003&Rsun&
Red&=&50&A/m2&
black=&op(cal&
grey&=&Hard&XLray&
Power&per&unit&area&~&1011L1012&erg&sL1&cmL2&
This&is&a&large&perturba(on!&
Op(cal/UV/EUV&also&&produced&at&the&
footpoints.&
Typically&a&flare&has&~2&strong&hard&XLray&
‘footpoints’&L>&nonLthermal&electrons&
Impulsive&phase&morphology&
Current&density&
Demonstrate&that&energy&is&stored&low&in&atmosphere&
(<&0.01&Rsun),&close&to&polarity&inversion&line.&&
Methods&for&calcula(ng&nonLpoten(al&fields&becoming&
quite&advanced,&though&s(ll&have&problems&
Prior&to&a&flare,&energy&is&stored&as&currents&in&the&corona&
Krucker&et&al.&&2008&
Fletcher&et&al.&&2007&
SXT Thin
Al.
HXT
Lo
Warren (2006)
50 individual
events
Flare&decay&(me&is&determined&by&singleLloop&cooling&proper(es&and&overall&
loop&excita(on&sequence&
A&becer&agreement&between&flare&EUV/SXR&(me&profiles&is&obtained&for&
mul(ple&loops&(e.g.&Reale&et&al&2004.,&Warren&2006,&Reale&et&al&2012,&etc.)&
Larger&solar&flares&involve&mul(ple&resolvable&loops,&excited&at&different&(mes.&
Mul(ple&loops&
• &Indicates&regions&of&stronger&and&weaker&
energy&input&&
L&probably&related&to&magne(c&
topology&
• &Hard&XLray&and&op(cal&sources&loca(ons&
are&a&subset&of&the&UV/Hα&ribbon&
loca(ons&
• &Can&be&4&ribbons&in&quadrupolar&field&
geometries&
• &Most&flares&organised&into&2&main&
ribbons&of&emission,&bright&in&Hα,&UV,&
EUV&
Impulsive&phase&morphology&
Flare&effects&on&deep&atmosphere&
t
Flare&(me&
Hard&XLrays&
Kosovichev&&&Zharkova&(1996)&
Requires&~ 0.1%&of&flare&energy&to&
penetrate&photosphere&
Sunquakes&
• &Most&high&energy&bremsstrahlung&is&produced&in&the&dense&chromosphere.&
• &In&the&chromosphere,&Eelectron&>>&E&target,&and&bremsstrahlung&is&very&inefficient.&&
• &Only&~&10L5&of&the&electron&energy&is&radiated&as&HXRs&&
• &Inferred&number:&1035L1036&electrons/s&accelerated&(would&empty&flare&corona&in&10s)&
These&are&the&primary&diagnos(c&for&flare&electrons.&
Hard&XLrays&observed&by&RHESSI&are&electronLproton&bremsstrahlung&from&
energe(c&electrons&(>&25keV).&
(Sudol&&&Harvey&2005)&
B&
Photospheric&LOS&field&changes&of&
typically&~100&G&coincident&in&space&&&
(me&with&impulsive&phase&
NonLreversing&field&changes&
There&is&evidence&that&deep&layers&of&the&solar&atmosphere&are&affected:&
400 G
Fo
E min 2−δ
δ −2
Gamma&rays&
so&lower'limit'on&P&is&determined&
Only&upper'limits'can&be&set&on&Emin&
Fit&parameters&from&observa(ons:&
Nonthermal:&&&&Fo, δ (= γ+1),&&&Emin&
Thermal:&T,&EM&
Assump(ons:&&
• &&2&dis(nct&electron&popula(ons&–&thermal&&&
nonLthermal&
• &&NonLthermal&emission&generated&by&
collisionallyLstopped&electrons&in&a&cold&target&&
Produc(on&of&nuclear&deLexcita(on&lines&
Others:&&The&positron&annihila(on&line&at&511keV&&
Con(nuum&γLrays&by&bremsstrahlung&(~&10MeV)&
&
&&&
L&shows&loca(on&of&10s&of&MeV&ions&
Neutron&capture&line&at&2.23&MeV&L&n(p,γ)D&
&Nuclear&deLexcita(on&lines&caused&by&
&bombardment&of&nuclei&by&>&30MeV&
protons&
The&presence&of&accelerated&ions&in&flares&is&revealed&by&gammaLrays&
€
flare&power&=&& P ( > E min ) =
Slope = γ&
Image: Iain Hannah
7-Aug-2010@18:09
Electron&spectral&fing&is&the&basic&way&we&currently&assess&solar&flare&energe(cs.&
Electron&spectra&
(rate&~&1036&e/s&⇒&essen(ally&all&electrons&from&the&corona&local&to&a&flare&are&
accelerated&within&10s.&But&the&accelera(on&can&last&for&minutes.)&
All&of&the&above&can&produce&electrons&of&a&high&energy&in&a&short&(me,&but&
none&can&readily&maintain&the&rate&implied&by&observa(ons.&
&L&generated&in&an&MHD&shock&(e.g.&CME&driven)&
&L&resul(ng&from&smallLscale&EM&or&electrosta(c&turbulence&
&L&generated&by&locally&increased&resis(vity&in&a&loop&(E&=&ηj)&
&L&due&to&changing&B&in&or&near&reconnec(on&(∇×E&=&L&∂B/∂t)&
Theories&for&the&origin&of&the&accelera(on&electric&field&include:&
Analysis&of&flare&XLrays&and&whiteLlight&shows&that&around&1036L1037&electrons&per&
second&must&be&accelerated&to&10s&of&keV&(and&a&similar&number&of&ions).&This&is&a&
significant&problem.&
Par(cle&accelera(on&in&flares&
Radio&frequency&=&plasma&frequency&
Type&II&bursts&are&produced&by&electrons&accelerated&at&a&superLAlfvenic&
coronal&shock&wave,&driven&by&a&coronal&mass&ejec(on.&
L produced&by&flareLaccelerated&electron&beams&streaming&into&space&&which&
generate&Langmuir&waves.&These&modeLconvert&to&EM&radia(on.&
Type&III&bursts&drir&rapidly&from&high&to&low&frequency.&
Coronal&radio&signature&&
of&flare&beams&and&shocks&
FDRAG
B&
total&poten(al&drop&=&1010&V&&
L~109cm&
E
Here,&efficient&par(cle&accelera(on&&can&
occur&–&but&only&in&a&small&volume&&(radius&~&
rL)&
Near'XPline'or'current'sheet,&there&may&be&an&
‘unmagne(sed’&region&B(x,y)&→&0,&or&a&
component&&of&E&parallel&to&B&&
But&E&⊥&B&almost&everywhere.&Leads&to&drirs&
rather&than&accelera(on&
Inferred&values&of&reconnec(on&electric&field&are&~&1&V/cm&
Observa(ons&suggest&that&high&electric&fields&occur&in&reconnec(on&
regions.&
DC&electric&fields&in&a&current&sheet&
FE
electron beam
• &Electrons&with&speeds&greater&than&a&cri(cal&speed&=vTe&(Ed/E)1/2&are&&
&&freely&accelerated&→&‘runaway’&electrons&
•  Ed typically&10L4&V/cm&
• &Electrons&accelerated&if&this&DC&field&is&greater&than&the&Dreicer&field, Ed
The&Dreicer&field&is&the&value&of&the&DC&field&such&that&the&force&exerted&&
&&on&the&electrons&exceeds&drag&force&from&eLe&Coulomb&collisions&
• &For&example,&a&local&increase&in&resis(vity&in&a&current&loop&leads&to&&
&&large&poten(al&drop&(since&huge&inductance&of&circuit&prevents&rapid&&
&&change&in&current)&&
FieldLaligned&DC&fields&
Liu&et&al&(2010)&
Closing&thoughts&
But&process&is&rather&inefficient&&
(~&1&in&104&par(cles&accelerated)&
Answering&these&will&involve&the&detailed&&plasma&physics&which&has&been&painfully&
learned&in&lab&and&magnetospheric&plasmas…take&every&opportunity&to&learn&about&
these&other&fields!&
• &&&&&How&do&we&extend&our&understanding&of&2LD&reconnec(on&to&3LD?&
• &&&&&How&do&we&(e&together&the&MHD&and&kine(c&theory?&
• &&&&&Are&our&trusted&old&models&for&flare&energy&transport&s(ll&viable?&
Some&formidable&challenges&ahead,&e.g.:&
Understanding&them&requires&harnessing&all&branches&of&plasma&physics&(along&with&
nuclear&and&atomic&physics,&radia(ve&transfer…&etc)&
Solar&flares&affect&all&layers&in&the&solar&atmosphere&and&produce&radia(on&and&
par(cles&right&across&the&spectrum.&
Miller&&&Viñas&(1993)&
In&principle&can&operate&
throughout&a&large&volume,&and&
accelerate&many&par(cles.&
Energy&can&be&lost&or&gained&in&
each&interac(on,&but&overall,&
energy&of&par(cle&increases&
Par(cle&resonates&with&highLfrequency&wave.&If&a&wave&spectrum&exists,&it&can&
‘hop’&stochas(cally&from&one&resonance&to&another&
Stochas(c&resonant&accelera(on&