1. Heliosphere - Lecture 8 November 08, 2005 Space Weather Course Electromagnetic Radiation in the Heliosphere Radio Emission Numerical studies of CME Acceleration and Transport of Particles SEP in Shocks Chapter 7 - Kallenrode (Energetic Particles in the Heliosphere)

2. Overview of what we saw in Lectutre 07
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?)
@P.Frisch
Overview of what we saw in Lectutre 07

3. Today: Electromagnetic Radiation in the Heliosphere:
Page (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)

4. Electromagnetic Radiation in the Heliosphere
Figure 6.21 Kallenrode
Impulsive and Gradual Events
On Radio Emission: type II and plasma frequency
SHOW uma imagem shel WIND

5. Electromagnetic
Radiation in different
Frequency ranges shows
typical time profiles.
Impulsive phase is related to an impulsive energy release,
probably reconnection, inside a closed magnetic field loop.

6. Soft X-Rays and H: Hard X-Rays: Gamma-Rays:
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.

7. 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.

8. Type II burst
The 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.

9. Another example: Halloween events
(WIND data)

10. Coronal Mass Ejection-numerical studies (Manchester et al. )
Should I mention the work of Hunhadsen…about detecting shocks….

11. Halloween-inserting magnetograms
Compare with
ACE data

12. CME 2 hours after the eruption (the Purple lines emanate from the AR)
Close-up of the flux
Rope inserted
The field lines are colored
by the velocity-the flux rope added
is shown with white field lines
CME 2 hours after the eruption (the
Purple lines emanate from the AR)

13. 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.

14. 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
Which ones are the most hazardous? Weidenbeck/Giacoloni/

15. 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.

16. Energetic Storm Particles (ESPs)
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.

17. Energy spectra of different ions species in the heliosphere

18. 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

19. 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)
In a medium at rest the Diffusion Equation: (it can be shown-
Kallenrode “Interplanetary Transport” chapter) that
Q is the source

20. 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
Where u is the velocity of the convective flow. So the continuity equation reads:
Pitch Angle Diffusion: In a plasma, fast particles are more likely
to 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.

21. 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).

22. 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.

23. 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.

24. 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 (BxB) The direction of the drift depends on the charge of the particle and is always such that the particle gains energy.

25. The abscissa shows the distance from the shock in gyro-radii
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.

26. Diffusive Shock Acceleration
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
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.

27. 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.

28. 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.

29. Self-Generated Turbulence:
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.

30. 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.

31. 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

32. 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.

33. 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.

34. Observed Power-law spectra
Other power laws here
Mason et al., 1999

35. 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

36. Large CME-related SEP events
Reames.SSR, 1999

37. Particle Acceleration at the Earth’s bow shock (recent Cluster observations)
Kis et al. (2004)

39. Corotating Interaction Regions
Ulysses data
Compression of the
magnetic field within CIR.
Slow, intermediate, and fast
wind and both a Forward (F)
and Reverse (R) shock.
Energetic Particles peaking at
The F/R shocks, with a larger
intensity at the reverse shock.
HISCALE data courtesy Tom Armstrong

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

41. Most IP shocks do not accelerate particles --
how well is this really understood?
Slide Courtesy of Glenn Mason

42. Effect of Large-Scale Turbulent Interplanetary Magnetic Field
Self-consistent plasma simulation

43. 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)

44. Magnetic Reconnection
Tanuma and Shibata, ApJ, 628, L77, 2005

45. Acceleration by Gradual Compressions (no shocks)
Not a shock !

46. What is the Acceleration Mechanism? Diffusive Shock Acceleration
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

47. Actual Particle Orbits
Decker, 1988

48. Parker’s energetic-particle transport equation
advection diffusion drift energy change

49. Diffusive Shock Acceleration
Solve Parker’s transport equation for the following geometry

50. The steady-state solution for , for an infinite system, is given by
Kennel et al, 1986
The downstream distribution is power law with a spectral index that depends only on the shock compression ratio!

51. Note that the dependence on compression ratio is not that strong
J ~ E (r = 2)
J ~ E (r = 3)
J ~ E (r = 4) – hardest
Reames.SSR, 1999

52. 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

53. 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.
Mason et al., 2004
Tylka et al 2005

54. 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

55. 2 related questions: What is the maximum energy
2 related questions: What is the maximum energy ? How rapidly can the particles be accelerated?

56. 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

57. 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)

58. Acceleration time
(Brms/B)2
Particle source
Characteristic Energy
Termination shock
(100 AU)
~ year
~0.3-1
IS pickup ions
H, 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
~ 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

59. 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.

60. 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.
t = 6 minutes at 7 solar radii
(B = Gauss)
Test-particle simulations of particles encountering shocks moving in weak large-scale magnetic-field turbulence (Giacalone, 2005)

61. SEPs from CME-Driven Shocks
In the corona
In interplanetary space

62. How are the particles transported to an observer?

63. Interplanetary transport of SEP events ACE/ULEIS observations
Impulsive-flare-related event
showing intensity variations
Gradual-flare-related event
showing no intensity variations

64. Numerical Simulations and simple interpretation of SEP transport

65. 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?

66. 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

67. Time-variation of SEP fluxes
Combined CME/MHD + Particle Transport/Acceleration Modeling
Schematic view of CME & Magnetic Field
Time-variation of SEP fluxes
Courtesy J. Kota

68. 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.