Heliosphere - Lecture 8November 08, 2005 Space Weather Course

Electromagnetic Radiation in the HeliosphereRadio EmissionNumerical studies of CMEAcceleration and Transport of ParticlesSEP in ShocksChapter 7 - Kallenrode (Energetic Particles in the Heliosphere)

@P.Frisch

What we saw:

-Corotating interaction regions(what are they? How do they form?)

-CMEs in the interplanetary space (magnetic clouds),(How CMEs propagate in the heliosphere)

-Interplanetary shocks(CMEs pile up material forming shocks-how those shocks propagate in space)

-Shock Physics(what happens at a shock?)

Today:• Electromagnetic Radiation in the Heliosphere: Page 131-134 (new edition) of Kallenrode• Coronal Mass Ejections (numerical studies)• Energetic Particles in the Heliosphere (Kallenrode

Chapter 7 - new edition & some material from conference) [Galactic Cosmic Rays, Solar Energetic Particles (SEPs), Energetic Storm Particles (ESPs)]

• Transport of Particles (Kallenrode)• Diffusive Shock Acceleration (Kallenrode)

Electromagnetic Radiation in the Heliosphere

Figure 6.21 Kallenrode

Impulsive and Gradual Events

Solar particle release (“SPR”) times, radio onset, and CME observations, compared to hard x- or -ray time profiles (left axis) and soft x-rays (right axis)

• ElectromagneticRadiation in different Frequency ranges showstypical time profiles.

Impulsive phase is related to an impulsive energy release, probably reconnection, inside a closed magnetic field loop.

• Soft X-Rays and H:In solar flare most of the electromagnetic radiation is emited as soft X-rays with

wavelength between 0.1 and 10nm(Soft X-Rays originate as thermal emission in hot plasmas with T~107K.Most of radiation is continuum emission. (lines of highly ionized O, Ca, Fe are

also present)H emission is also a thermal emission.• Hard X-Rays:Hard X-Rays are photons with energies between a few tens of keV and a few

hundred keV generated as bremsstrahlung of electrons with slightly higher energies. Only a very small amount of the total electron energy is converted into hard X-Rays

• Gamma-Rays:Gamma-ray emission indicated the presence of energetic particles. The spectrum

can be divided into three pars: (a) Bremsstrahlung of relativistic electrons; (b) Nuclear radiation of excited CNO nuclei leads to a gamma-ray spectrum in the range of 4 to 7MeV; c ) Decaying pions lead to gamma-ray continuum emission above 25MeV.

• Radio Emission:Electrons streaming through the coronal plasma excite Langmuir oscillations. Near

the sun the wavelength are in the meter range. In the interplanetary space the radio burst are kilometric bursts. The bursts are classified depending on their frequency drift. The type I radio burst is a continuous radio emission from the Sun, basically the normal solar radio noise but enhanced during the late phase of the flare. The other type of bursts can be divided in fast and slow drifting bursts or continua:

Type III radio burst starts early in the impulsive phase and shows a fast drift towards lower frequencies. Since the frequency of the langmuir oscillation depends on the density of the plasma ( )

The radial speed of the radio source can be determined from this frequency drift using a density model of the corona.

The speed of type III is about c/3 it is interpreted as stream of electrons propagating along open field lines into interplanetary space. Occasionally the type III burst is suddenly reversed, indicating electrons captured in a closed magnetic field loop: as the electrons propagate upward, the burst shows the normal frequency drift which is reversed as the electrons propagate downward on the other leg of the loop.

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ω pe= 0.564 ne rad /s

• Type II burstThe frequency drift is much slower indicating a radial propagation speed

of its source of about 1000km/s. It is interpreted as evidence of a shock propagating through the corona. It its not the shock itself that generated the type II burst but the shock accelerated electrons, As these electrons stream away from the shock, they generates small type III structures, giving the burst the appearance of a herringbone in frequency time diagram with the type II as the backbone and the type III structures as fish-bones. The type II burst is split into two parallel frequency bands interpreted as forward and reverse shocks.

Plot showing showing the frequency range of the metric-DH-kilometric (Nov 04, 1997 event 6-8hrs taken from the Coordinate Data Analysis CDA) taken from RAD1 and RAD2, and ground base observatories. Note the frequency decreases with time as the shock propagates outward and the ambient density decreases.

• Another example: Halloween events

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(WIND data)

Coronal Mass Ejection-numerical studies (Manchester et al. )

Halloween-inserting magnetograms

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Compare withACE data

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The field lines are coloredby the velocity-the flux rope addedis shown with white field lines

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Close-up of the flux Rope inserted

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CME 2 hours after the eruption (the Purple lines emanate from the AR)

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After 65 hours of simulation. CME is shown as a white isosurface of density enhancement of a factor 1.8 relative to the original steady state solution. The magnetic field lines are shown in magenta.The CME is about to reach the Earth which is at the center of the orange sphere on the right.

Energetic Particles in the Heliosphere• Galactic Cosmic Rays (GCR), Anomalous Cosmic Rays (ACR), Solar

Energetic Particles (SEPs), Energetic Storm Particles (ESPs)

Energies ranges from supra-thermal to 1020 eV

• Galactic Cosmic Rays (GCR)Energies extending to 1020 eV. The are incident upon the heliosphere uniformly

and isotropically. In the inner heliosphere, the galactic cosmic rays are modulated by solar activity: the intensity of GCRs is highest during solar minimum and reduced under solar minimum conditions.

• Anomalous Cosmic Rays (ACR)Energetically connected to the lower end of the GCRs but differ from them with

respect to composition, charge states, spectrum, and variation with the solar cycle. As neutrals particles of the interstellar medium travel through the interplanetary space towards the Sun, they become ionized. These charged particles then are convected outward with the solar wind and are accelerated at the Termination Shock. Then they propagate towards the inner heliosphere where they are detected as anomalous component.

• Solar Energetic Particles (SEPs) They are accelerated in flares, CMES (?). The injection of these particles into the

heliosphere is point-like in space in time.

• SEP energies extend up to tens-GeV. The ones with GeV can be observed in neutron monitors on the ground, and the event is called ground-level event (GLE). Owing to interplanetary scattering the particle events last between some hours and a few days. SEP events show different properties, depending on whether the parent flare is gradual or impulsive. In gradual events the SEP mix with particles accelerated at the shock.

• Energetic Storm Particles (ESPs) Originally ESPs were though to be particle enhancements

related to a passage of an interplanetary shock. ESPs are particles accelerated at interplanetary shocks.

Energy spectra of different ions species in the heliosphere

Transport of Particles• Spatial Diffusion: consequence of frequent, stochastically

distributed collisions. Instead of individual particles we will consider an assembly of particles, described by the distribution function.

• Diffusion is not only spatial diffusion. It can be diffusion in momentum space (e.g. enhance of temperature, energy…)

Spatial Diffusion (Drunkyards):(steps of length )The average spatial displacement is

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Δx 2 = Nλ2

• If the particle as a speed v, the total distance s traveled during a time t is s=vt=N and

where D is the diffusion coefficient (1D)

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Δx 2 = Nλ2 = vλ t = 2Dt

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D = 12

vλ

In a medium at rest the Diffusion Equation: (it can be shown-Kallenrode “Interplanetary Transport” chapter) that

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∂ρ∂t

− DΔρ = Q(r,t)

Q is the source

• Diffusion-Convection Equation:If the particles are scattered in a medium that is moving..in our case the

convection is due to the solar wind: the particles are scattered at inhomogeneities frozen in the solar wind and propagating with the solar wind. In this case the streaming of particles is

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S = ρr u − D∇ρ

Where u is the velocity of the convective flow. So the continuity equation reads:

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∂ρ∂t

+∇(ρr u ) =∇(D∇ρ )

Pitch Angle Diffusion: In a plasma, fast particles are more likelyto encounter small-angle interactions. Thus to turn a particle around, a large number of interactions is required.In space plasmas small-angle interactions are not due to Coulomb-scattering but due to scattering a the plasma-waves.Let assume a magnetized plasma and regards the energetic particles as test particles.The particles gyrate around the lines of force and a pitch angle can be assigned to each particle: =cos.

• Each interaction leads to a small change in ->diffusion in pitch angle space. So now the spatial diffusion is written as:

• Where is the pitch angle diffusion coefficient. The scattering can be different for different pitch angles (different waves available for wave-particle interaction). The transport equation can be written as:

• Where f/s is the derivative along the magnetic field line.• We also have to include diffusion in momentum space: collisions can

change not only the particle direction but also its energy.

Where Dpp is the diffusion coefficient in momentum space. (the second term describes ionization-non-diffusive changes in momentum)

(the physics of the scattering process is hidden in Dpp).

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∂∂

(μ) ∂f∂μ

⎛ ⎝ ⎜

⎞ ⎠ ⎟

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∂f∂t

+ μv ∂f∂s

= ∂∂μ

κ (μ) ∂f∂μ

⎛ ⎝ ⎜

⎞ ⎠ ⎟

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Sp = −Dpp∂f∂p

+ dpdt

f

• Wave-particle interactions: non-liner theory-no general algorithms exist.• Quasi-linear Theory: its based on perturbation theory; interactions between waves and

particles are considered to first order only. All the terms in second order in the disturbance are ignored. So only weakly turbulent wave-particle interactions can be treated this way. We assume that the plasma to be a self-stabilizing system: neither indefinite wave growth happens nor are the particles trapped in a wave well.

• The basic equation that describes the evolution of a distribution particles is the Vlasov equation:

• If you split the quantities in a slowly evolving average part f0,E0,B0 and a fluctuating part f1,E1, and B1 where the long term averages of the fluctuating quantities vanish we get:

• Where the term on the right-hand side describes the interaction between the fluctuating fields and the fluctuating part of the particle distribution. This term has a nature of a Boltzman collision term. These collisions result from the non-linear coupling between particles and wave fields.

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∂f∂t

+r v ⋅∇f + q

m

r E +

r v ×

r B

c

⎛

⎝ ⎜

⎞

⎠ ⎟⋅∂f∂v

= 0

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∂f0

∂t+

r v ⋅∇f0 + q

mv × B0 ⋅

∂F0

∂v= − q

mE1 + v × B1( ) ⋅∂f1

∂v

Particle Acceleration at Shocks• There are different physical mechanisms involved in the particle acceleration in

interplanetary shocks:• The shock drift acceleration (SDA) in the electric induction field in the shock front• The diffusive shock acceleration due to repeated reflections in the plasmas converging

at the shock front;• The stochastic acceleration in the turbulence behind the shock front.The relative contribution of these mechanisms depends on the properties of the shock:

SDA is important for perpendicular shocks where the electric induction field is maximal; but vanishes in parallel shocks. Stochastic acceleration requires a strong enhancements in downstream turbulence to be effective; while diffusive acceleration requires a sufficient amount of scattering in both upstream and downstream media. In addition shock parameters such as compression ratio; speed; determine the efficiency of the acceleration mechanism.

Usually the particles are treated as test particles: they do not affect the shock; and effects due to the curvature of the shock are neglected.

• Shock Drift Acceleration (SDA)• Scattering is assumed to be negligible, to allow for a reasonable long drift

path. Its necessary though that the particles are feed back into the shock for further acceleration. In shock drift acceleration, a charge particle drift in the electric field induced in the shock front (in the shock rest frame):

• This field is directed along the shock front and perpendicular to both magnetic field and bulk flow. In addition the shock is a discontinuity in magnetic field strength (BxB) The direction of the drift depends on the charge of the particle and is always such that the particle gains energy.

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ρ E = −

r u u ×

r B u = −

r u d ×

r B d

The abscissa shows the distance from the shock in gyro-radii. In the left panel the particle is reflected back into the upstream medium. The other two shos particles transmitted through the shock. The energy gain of a particle is largest if the particle can interact with the shock front for a long time. This time depends on the particle’s speed perpendicular to the shock.

• The particle speed relative to the shock is determined by the particle speed, shock speed, pitch angle and the angle of the shock.

• The average energy gain is a factor 1.5-5. • Energy gain then to high energies will require repeated interactions between particles

and shock->scattering in turbulence.

• Diffusive Shock Acceleration • This is the dominant mechanism at quasi-parallel shocks. Here the electric

induction field in the shock front is small and shock drift acceleration becomes negligible. In diffusive shock acceleration, the particle scattering in both sides of the shock is crucial.

• The magnetic fields on both sides of the shock are turbulent. The diffusion coefficients upstream and downstream are Du and Dd..Where in SDA the location of the acceleration is well defined, in diffusive shock acceleration, the acceleration is given by the sum of all pitch angle scatters.

• Example: In the upstream medium the particle gains energy due to a head-on collision with a scatter center; in the downstream it loses energy because the scatter center moves in the same direction as the particle. Since the flow speed (and therefore the velocity of the scattering center) is larger upstream than downstream a net gain of energy results.

• The energy gain will depend on the velocity parallel to the magnetic field and on the pitch angle. The equation describing the “statistical” acceleration is:

From left to right: convection of particles with the plasma flow; spatial diffusion; diffusion in momentum space; losses due to particle escape from the acceleration region; and convection in momentum space due to ionization or Couloumb losses. The term on the right is a source term describing the injection of particles in the acceleration process.

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∂f∂t

+r

U ∇f −∇ ⋅(D ⋅∇f ) − ∇ ⋅r

U 3

p ∂f∂p

+ fT

+ 1p2

∂∂p

p2 dpdt ⎛ ⎝ ⎜

⎞ ⎠ ⎟ f

⎛ ⎝ ⎜

⎞ ⎠ ⎟= Q(p,r,t)

• In steady state f/t =0. If we neglect also (in first order the losses and convection in momentum) we get

• That the time required to accelerate particles from momentum p0 to p is:

• If we assume that the diffusion coefficient is independent of momentum, then we can get a characteristic acceleration time

In p(t)=p0exp(t/a). We can re-write this as:

• Where r=uu/ud the ratio of flow speeds in the shock rest frame. Here Dd/ud is assumed to be small compared to Du/uu.

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∂f∂t

+r

U ∇f −∇ ⋅(D ⋅∇f ) − ∇ ⋅r

U 3

p ∂f∂p

= Q( p,r,t)

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t = 3uu − ud

dpp

Du

uu

+ Dd

ud

⎛ ⎝ ⎜

⎞ ⎠ ⎟

po

p

∫

€

=p

dp /dt= 3

uu − ud

Du

uu

+ Dd

ud

⎛ ⎝ ⎜

⎞ ⎠ ⎟

€

=3r

r −1Du

uu2

• The energy spectrum expected from diffusive shock acceleration is a power law:

• With (in the non-relativistic case)

• Why do we get a power law? The energy gain for each particle is determined by its pitch angle and the number of shock crossings

(that is stochastic). For high energy gains the particle must be “lucky” to be scattered back towards the shock again and again. Most particles make a few shock crossings and then escape into the upstream medium. The stochastic nature of diffusion allows high gains for a few particles, while most particles make only small gains.

• Self-Generated Turbulence:Whenever energetic particles stream faster than the Alfven speed, the generate and amplify MHD waves

with wavelengths in resonance with the field parallel motion of the particles. These waves grow in response to the intensity gradient of the energetic particles.

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J(E) = J0E −γ

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γ=12

r + 2r −1

• M. Lee developed a theory that suggest that: first the accelerated particles stream away from the shock. As they propagate upstream, the particles amplify low-frequency MHD waves in resonance with them. Particles escaping from the shock at a later time are scattered by these waves and are partly reflected back towards the shock. These latter particles again interact with the shock, gaining additional energy. The net effect is an equilibrium between particles and waves which in time shifts to higher energies and larger wavelengths.

• In resume: a shock is a highly non-linear system. Either approximations are used to solve it analytically or studied by means of numerical simulations.

• The rather smooth transition between the maxwellian and the power law is in agreement with the assumption that the particles are accelerated out of the solar wind plasma

• Low-energy particles: • The three types of acceleration mechanism can be distinguished

• At High-energy particles (MeV): the different spectra do not reflect the local acceleration mechanism but the location of the observer relative to the shock. This is a consequence of the higher speeds of the MeV particles that allows them to escape from the shock front. An observer in the interplanetary space samples all the particles that the shock has accelerated on the observer’s magnetic field line while its propagates outward.

Evidence of shock acceleration• Indirect evidence:

– Energetic particles in space share one common characteristic:

• energy spectra are often Power Laws • Diffusive shock acceleration theory naturally

explains this • spectral exponents should vary little from one event

to the next.

• Direct evidence:– Numerous observations of energetic particles

associated with shocks• Observations of shocks with no accelerated particles

too. This is not well understood.

Other power laws here

Observed Power-law spectra

Mason et al., 1999

• Anomalous Cosmic Rays and the Termination Shock– Accelerated interstellar pickup ions– Low charge states (+1) imply that they are accelerated rapidly (about 1 year).– The best explanation for this is acceleration by a termination shock that is nearly

perpendicular over most of its surface (Jokipii, 1992)

Decker et al., Science, 2005

Large CME-related SEP events

Reames.SSR, 1999

Particle Acceleration at the Earth’s bow shock (recent Cluster observations)

Kis et al. (2004)

Compression of themagnetic field within CIR.

Slow, intermediate, and fast wind and both a Forward (F) and Reverse (R) shock.

Energetic Particles peaking atThe F/R shocks, with a largerintensity at the reverse shock.

Ulysses data

HISCALE data courtesy Tom Armstrong

Corotating Interaction Regions

A simple interpretation of the higher intensities at the reverse shock of a CIR 2-shock pair

• Forward shock – pickup ions are from slow solar wind

• Reverse shock – pickup ions are from the fast wind– Sart with higher energy– More efficient acceleration

• This is relevant to our understanding of SEP events also.

Giacalone and Jokipii, GRL, 1997

Most IP shocks do not accelerate particles --how well is this really understood?

Slide Courtesy of Glenn Mason

Effect of Large-Scale Turbulent Interplanetary Magnetic Field

Self-consistent plasma simulation

Where do shocks exist?

• Direct observations of collisionless shocks have been made since the first observations of the solar wind by Mariner 2.

• The Earth’s bow shock has been crossed thousands of times

• Theoretically, we expect shocks to form quite easily. – In the solar corona, shocks can

form even when the driver gas is moving slower than the characteristic wave speed. (Raymond et al., GRL, 27, 1493, 2000)

Tanuma and Shibata, ApJ, 628, L77, 2005

Magnetic Reconnection

Acceleration by Gradual Compressions (no shocks)

Gradual Compression Not a shock !

• Discovered by four independent teams:

– Bell (1978), Krymsky (1977), Axford et al (1977), Blandford & Ostriker (1978)

• Requires that particles diffuse across a diverging flow (a shock)

• Also requires some form of trapping near the shock

What is the Acceleration Mechanism?Diffusive Shock Acceleration

Actual Particle Orbits

Decker, 1988

Parker’s energetic-particle transport equation

advection diffusion drift energy change

Diffusive Shock Acceleration

• Solve Parker’s transport equation for the following geometry

• The steady-state solution for , for an infinite system, is given by

The downstream distribution is power law with a spectral index that depends only on the shock compression ratio!

Kennel et al, 1986

Note that the dependence on compression ratio is not that strong

J ~ E-2 (r = 2) J ~ E-1.25 (r = 3)J ~ E-1 (r = 4) – hardest

Reames.SSR, 1999

Electrons

• In principal, there is no difference between electrons and ions in the basic picture of DSA– What scatters the electrons?

• Importance of large-scale fluctuations– Electrons move rapidly nearly along magnetic lines of

force that can intersect the shock in multiple locations

Heavy Ions• Heavy ions can also be accelerated efficiently by shocks.

• Particles of a given species with a higher charge state are accelerated faster, and hence, can reach a higher total energy.

Tylka et al 2005 Mason et al., 2004

The “injection problem”• What is the particle source?

– Solar wind ions can be accelerated by shocks

• However, composition of SEPs are NOT consistend t with solar wincomposition.– A simple interpretation is given

at the right

2 related questions:

What is the maximum energy ?

How rapidly can the particles be accelerated?

Spectral cutoffs and rollovers

• Finite acceleration time Parallel shocks slow Perpendicular shocks fast

• Free-escape losses• Limits imposed by the size of the

system

All lead to spectral variations that depend on the transport parameters (e.g. species, magnetic turbulence, etc.) will cause abundance variations that depend on species, and vary with energy

Acceleration Time in Diffusive Shock Acceleration

• The acceleration rate is given by:

Hence, the maximum energy depends strongly on both the shock speed and on the level of magnetic turbulence (which is not well known near the Sun)

Acceleration time (Brms/B)2 Particle source Characteristic Energy

Termination shock (100 AU)

~ year ~0.3-1 IS pickup ionsH, He, N, O, Fe (mostly)

~ 200 MeV (total energy)

CIRs (2-5 AU)

~ months ~0.5 Pickup ions, solar wind, enhanced C/O

~ 1-10 MeV/nuc

Earth’s bow shock (1 AU)

~tens of minutes ~1 Pickup ions, solar wind, magnetosphere ions

~ 100-200 keV/nuc.

Large SEPs (r > 0.01 AU)

Minutes or less ?? Suprathermals *H (mostly), He, and heavy ions, even M > 50

~1 MeV/nuc, sometimes up to ~20 GeV

Transient IP shocks

days ~0.3 Suprathermals

Less than ~1 MeV

* Suprathermals pervade the heliosphere – their origin is not well understood

Perpendicular vs. Parallel Shocks

• The acceleration time depends on the diffusion coefficient

• because , the acceleration rate is higher for perpendicular shocks

– For a given time interval, a perpendicular shock will yield a larger maximum energy than a parallel shock.

• Perpendicular Shocks:

– The time scale for acceleration at a perpendicular shock is 1-2 orders of magnitude shorter (or possibly much more) than that at a parallel shock.

Test-particle simulations of particles encountering shocks moving in weak large-scale magnetic-field turbulence (Giacalone, 2005)

t = 6 minutes at 7 solar radii (B = 0.003 Gauss)

SEPs from CME-Driven Shocks

In the corona In interplanetary space

How are the particles transported to an observer?

Interplanetary transport of SEP eventsACE/ULEIS observations

Impulsive-flare-related eventshowing intensity variations

Gradual-flare-related eventshowing no intensity variations

Numerical Simulations and simple interpretation of SEP transport

How do particles escape from closed-field regions?

• Not well understood.• Observations indicate that

energetic electrons (producing radio bursts) are probably on open field lines

• Reconnection with open fields?

• Cross-field diffusion?

Important Questions

• What is the temporal evolution of the shock-accelerated intensity and spectra ?– Observations made at 1AU are an “integral

• What are the sources ?– Probably the most important question with regards to Space-Weather

forecasting

• What is the shock geometry (especially back near the Sun) ?– Parallel and perpendicular shocks have different shock-acceleration

physics

• What is nature of the particle transport ?– Need to know the form of the magnetic-field power spectrum,

especially near the acceleration site

Time-variation of SEP fluxes

Courtesy J. Kota

Schematic view of CME & Magnetic Field

Combined CME/MHD + Particle Transport/Acceleration Modeling

Conclusions

• Shocks provide a natural explanation for most cosmic rays (including SEPs).

• The rate of acceleration (especially by perpendicular shocks) is sufficiently high to explain the existence of > GeV/nuc SEP events.

• Shocks are common in space plasmas. They have been observed to form very close to the Sun and are expected to form very easily.