1. Heliosphere - Lectures 6 October 04, 2005 Space Weather Course Corotating Interaction Region, Magnetic Clouds, Interplanetary Shocks, Shocks and Discontinuities Chapter 6-Gombosi (Shocks and Discontinuities) Chapter 6 - Kallenrode (The Solar Wind) (Shock Waves 6.8) (extra reading Landau and Lifschitz-)

2. Overview of what we l saw in Lecture 05 @P.Frisch -What we saw: -Solar wind formation and acceleration -Interplanetary magnetic field

3. @P.Frisch Today: -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?)

4. Corotating Interaction Regions Fast and slow streams. The frozen-in magnetic field is carried Is wound up to a spiral. In a slow stream the field is curved more strongly than in a fast one. Since the field lines are not allowed to intersect, at a certain distance from the Sun, an interaction region develops between the fast and slow streams. Because this structure rotates with Sun, it is called corotating interaction region (CIR). At the sun there is an abrupt change in solar wind speed from fast to slow-the region of compressed at 1AU typically extends about 30 degrees. CIR tend to distort of even destroy all small scale fluctuations and Disturbances propagation outward from the Sun. When CIR and travelling interplanetary shocks interact, merged Interacting regions results.

5. Magnetic Clouds How CMEs propagate in Space (how CME share its energy?) Magnetic cloud, of helical field lines, shown propelled from the Sun as part of an coronal mass ejection. The cloud travels through the solar wind and eventually, if moving in the right direction, engulfs the Earth's magnetic field The magnetic field lines in the magnetic cloud (shown in red with a helical geometry) are unusually very strong compared to the field that exists in the surrounding solar wind. That strong field is part of the reason for the storm. Also the dynamics of the cloud is controlled by its strong magnetic field and not by its internal gas pressure, which plays a bigger role in the normal solar wind surrounding the cloud. (Magnetic field acts like a pressure when pushing perpendicular to its own direction.) The cross-section of the magnetic cloud at its biggest part is typically about 200 times the diameter of the Earth's magnetosphere, at its largest cross-section, in the plane which usually contains the Earth itself.

6. Interplanetary Shocks Typical signatures of a magnetic Cloud can be summarized as follows: a)Decrease in Magnetic Field strength Inside the cloud; b) Rotation of the Magnetic field vector; c) Decrease in Plasma density, plasma speed, plasma Temperature (and therefore plasma Beta); and d) bi-directional streaming of Suprathermal electrons back and forth Along the length of the cloud. At the beginning of the cloud the magnetic Field is almost perpendicular to the plane Of the ecliptic. Inside the cloud the elevation Decreases until at the end the magnetic Field vector is almost opposite to the one At the beginning (B wrapped around The ejecta) How long B stays connected to the Sun?

7. Only one-third of CMEs drive an interplanetary shocks, while all the interplanetary shocks are driven by CMEs. Interplanetary shocks are indentified as sudden increase of density, speed, temperature and magnetic field. The basic properties of shocks between 0.3-1.0AU: Compression ratio varies between 1 and 8 Magnetic compression varies between 1 and 7 Shock speed between 300km/s-700km/s. Occasionally shocks speeds above 2000km/s are observed. The angular extent of the shock varies between few tens of degrees And up to 180. The shock is always wider than the driving CME. If a shock is very fast close to the Sun (with CME speeds Above a1000km/s it is likely to decelerate in the interplanetary space. If a shock is rather slow on the Sun to do not decelerate but Propagate at roughly constant speed. The difference is in the energy release mechasims: more explosive In fast shocks and CMEs; rather continuous in the slower ones. Fast shocks tend to be more efficient particle accelerators. The kinetic energy of the shock in converted in kinetic energy of the particles.

8. Shock Physics Chapter 6 - Gombosi What are shocks? Shocks and Discontinuities: transition layers where the state of the fluid changes from one that is near an equilibrium state to a different one. (Examples: Shocks, transition layers in the Interplanetary Medium, in the Sun) Transition layer is very narrow compared to the characteristic scale of the system

9. Examples of Shocks

10. What are shocks? A Shock is a discontinuity separating two different regimes in otherwise continuous medium. It is associated with a disturbance moving faster than the signal speed in the medium (in a gas the signal speed is the speed of sounds; in space plasma: alfven speed and the sound speed) At the shock front the properties of the medium change abruptly. In a hydrodynamic shock, pressure and density increase- in a magnetohydrodynamic shock, plasma density and magnetic field strength increase. Behind the shock front, a transition back to the properties of the undisturbed medium must occur. Behind a gas-dynamic shock - density and pressure decrease - behind a magnetohydrodynamic shock, plasma and magnetic field strength decrease. If the decrease is fast:a reverse shock develops.

11. The disturbance and the shock can be moving: traveling shock (mass ejections propagating from the Sun through the interplanetary space drive traveling shocks) Standing shock (planetary bow shocks: interplanetary bow shock) (in plasma we can have collisionless shocks: densities are too low to allow for collisions- instead the collective effects of the electric and magnetic properties of the plasma allow for frequent interactions and a formation of a shock wave). Shock: non-linear wave propagating Faster than the signal speed

12. Example of a shock: a large amplitude pressure pulse is created by an explosion. In the air-close to the site of the blast the sound speed can increase to 1000km/s. The signal does not propagate as a harmonic wave: the compressional phase the pressure amplitude Can exceed the atmospheric pressure. During decompression the pressure Cannot drop below zero. Thus the amplitude of the positive and negative half- Waves are different. For a large amplitude wave during compression wave can propagate faster While the other half propagate slowe- Thus the wave front steepen in time -if the steepening leads to a jump in density and Pressure a shock wave has formed ->in this case a Blast Wave (Type II radio burst in the solar corona ) Travelling shock: supersonic disturbance propagates Through the medium Standing shock: the object is at rest and the flow is supersonic

13. Collisionless Shock Waves Space plasma are so rarefied that the collisions are rare: electron and proton can have different temperatures; distribution functions very different from Maxwellian; presence of magnetic field can lead to highly anisotropic particle distributions; dissipation processes involving particle-field interactions. B acts as a coupling device (ideal MHD) but the details of the shock front the plasma immediately around it cannot be treated with MHD since MHD does not consider the motions of and the kindetic effects due to individual particles. Observations indicate that the collective behavior of the plasma is mainly due to wave-particle interactions. (collisionless shocks are an exanple of a macroscopic flow phenomenon regulated by microscopic kinetic processes).

14. Perfect gas: shock waves are discontinuities surfaces separating two distinct gas states (in reality the shock has a finite thickness ~ order of mean free path) (a shock is not a reversible process (it has to do with time and it’s ocurred instantaneously) Normal Shock Waves in a Perfect Gas: x flow Simplification : Also assumed that the shock wave us perpendicular to the flow direction (shock normal vector parallel to the flow) Also assumed that far upstream and far downstream the gas can be treated by a maxwellian in thermal equilibrium

15. Gas (no B) Euler equations (chapter 4 of Gombosi) (neglecting viscous force and the heat flow term) In steady-state (time derivatives=0) and one-dimensional: n(x):number density u(x):flow velocity p: pressure

16. Integrating: The energy equation can be rewritten (using the momentum equation):  is the specific heat = 5/3 Integrating the fluid equations (I)

17. Mach numbers Definining the Mach Number: (ratio of flow speed to sound speed) And eq. (I) can be written as (just substitution): Also-ratio of upstream to downstream temperatures: (manipulating Eq. (I)) Eq. (II)

18. Then Manipulating the continuit and momentum eqs. (you should do it!) Eq. (III) Eq. (IV) Combining Eq. (III) + (IV) we get an equation that connect Upstream and downstream Mach numbersl

19. The solutions are: (1) M 2 =M 1 that is trivial (no change in the flow!) The other solution is When M 1 This solution has a singularity  (Figure 6.1): the solution indicate that Normal shocks can only be formed in supersonic flows Eq.V With Eq. V we can re-write the previous eq’s to get the Rankine-Hugoniot relations:

20. What about MHD Shocks? Back to our favorite MHD equations (now ignoring the gravity) (and writing it in a conservative way density momentum energy magnetic field

21. Assumptions: Steady-State+Discontinuity planar+the quantities only vary in the perpendicular direction to the discontinuity In this case all these equations states that the total flux of mass, momentum, energy are conserved across the discontinuity (where “[]” indicate jumps across the discontinuity [A]=A 2 -A 1 ) These equations Describe the several types of MHD discontinuites

22. Contact and Tangential Discontinuities Case that there is no particle transport across the discontinuity This mean u 1n =u 2n =0 and the jump conditions become: The normal component of the magnetic field doesn’t change across the discontinuity

23. 1. When B n1 =B n2 =0 Tangential Discontinuity In this case This means the Density, Pressure and B(tangential) is discontinuous across the shock 2. When B n1 =B n2  0 Contact Discontinuity In this case This means that the velocity the B and p are continuous across the shock

24. When there is Transport Across: Called Shocks 1.Both the normal velocity and the density are continuous (and non Zero). This is called Noncompressive Shock and In this case the jump conditions become:

25. These equations can be combined to obtain: If the magnetic field changes across the shock ( ) Therefore the fluid velocity can only be Alfven speed Manipulating the shock equations you get: The shock propagates at the Alfven speed These shocks are called Alfven shocks or Intermediate shocks

26. Jumps in normal velocity and the density: Compressive Shocks (However the mass flux is conserved: ) In this case the jump conditions can be re-arranged to obtain: The direction of B t does not change across the shock but its magnitude change In this case there are two solutions for the jump conditions equations: v shock =v slow v shock =v fast Compressive shocks can have plasma flowing across the shock Slow shocks are characterized by decrease of B t across the shock Fast shocks are characterized by an increase of B t across the shock (CHASER et ha equ. 6.39-6.40)

27. Many solar wind discontinuities are tangential: in the absence of reconnection magnetopause is a tangential discontinuity; Of the shocks the most typical in solar system are fast shocks Earth’s bow shock is a fast shock as are most interplanetary shocks

28. Solar Energetic Particles and Acceleration of Particles…next class…