1. Acceleration of Anomalous Cosmic Rays at a Non Spherical Termination Shock
Abstract ID: SH21B-1919
Udara K Senanayake (uks0001@uah.edu ) , Vladimir A Florinski (vaf0001@uah.edu)
1 1
1
Physics/CSPAR, University of Alabama in Huntsville, Huntsville, AL
1. Introduction 3. Numerical Model 4. Results contd ...
● Anomalous Cosmic Rays (ACRs) are assumed to be accelerated at ● Same code used for Galactic Cosmic Rays (GCRs) in Florinski &
the Termination Shock (TS) . Shape of the TS is not yet known Pogorelov (2009) was adapted to the ACR acceleration. Difference is that
exactly. Most of the current simulations on ACRS are done using a trajectory exit points are in momentum space (T min) rather than in real
spherical TS. Here we use a blunt TS to study the ACR acceleration. space (heliopause). Shock strength of 3 was used.
● Voyager I and Voyager II are the two major spacecrafts collecting ● Transport is modeled using the Parker's equation (Parker 1965; Gleeson &
ACR data. Most theories made by scientist using a spherical shock Axford 1967), ∂f ∂f ∂f ∇ .u ∂f
didn't match up with the observation when Voyager I (V1) and
Voyager II (V2) crossed TS in 2004 and 2007 respectively.
∂t
∂
+(ui+v d , i)
∂ xi
−
∂ xi ( κij
∂ xj )
−
3 ∂ ln p
=0
∂ Bk
2. Background
● Drift velocity v d ,i =
pcw
3e
ϵ ijk
∂xj B ( )
2
● The blunt shock and the plasma velocities used in this model are w B0 Fig.9 Parker spiral in the ecliptic plane Fig.10 Average intensities at the TS
similar to Fahr (1993). The radius of the shock is given by, ● Diffusion (Czechowski et al. 2001) κ∥ = P κ⊥ = 0.01 κ∥ for 30MeV ACR particles
Fig.11 Energy spectra at the
c B
blunt TS
b
r=
√k
√ √ k cos θ+1−cos θ
2
where; w-particle velocity, P-rigidity in GeV, B 0-magnetic field at 1AU
5. Conclusions
● It is clear from above results that the TS is blunt and ACR acceleration is happening at the
where  is the spherical polar angle, b = 140 and k = 1.53 - 1 2 ● Here the stochastic particle trajectories are integrated backward in time
flanks of the TS which is similar to results of McComas & Schwadron (2006).
similar to works of Zhang (1999), Ball (2005) and Florinski & Pogorelov
● The plasma velocities are given by the following equations, (2009). ●Currently V1 ACR intensities decreasing may be due to leaking of particles through the
heliopause
2
4. Results
(
b
ur =a 2 −cos θ
r ) uθ =a sin θ uϕ =0 where a = 100
●V2 intensities increasing may be because it may be going towards flanks so as shown
above ACR intensities should increase.
Fig.1 Shape of the TS used Fig.2 Velocity magnitude plot with streamlines in the
ecliptic plane
● Inside the TS Magnetic Field behave as Parker Field, so the field
outside of the TS is calculated by integrating along streamlines.
Fig.5 Energy spectra - spherical TS Fig.6 Energy spectra at the nose – blunt TS
Fig.12 Voyager 1 observations (1) Fig.13 Voyager 2 observations (1)
6. Acknowledgments References
● (1) From Browse Data Plots link at http://sd-www.jhuapl.edu/VOYAGER/
● Ball, B., Zhang, M., Rassoul, H., & Linde, T. 2005, ApJ, 634, 1116
I would like to thank my adviser ● Czechowski, A., Fitchner, H., Grzedzielski, S., Hilchenbach, M., Hsieh, K. C., Jokipii, J. R., Kausch, T.,
Dr. V. Florinski for providing me ●
Kota, J., Shaw, A., 2001 A&A 368, 622
Fahr H. J., Fitchtner H., Scherer K., 1993, A&A 277, 249
with the code for the spherical TS ● Florinksi, V., & Pogorelov, N. V., 2009, ApJ, 701, 642
model and also for all the ● Gardiner, C. W. 1985, Handbook of Stochastic Differential Methods for Physics, Chemistry and the Natural
Sciences (Berlin: Springer)
guidance and support. ● Gleeson, L. J., & Axford, W. I., 1967, ApJ, 149, L115
Fig.3 3D cutout view of the ● McComas, D. J. and N. A. Schwadron, 2006, Geophys. Res. Lett. 33, 25437
calculated magnetic field Fig.4 Magnetic Field Lines (Parker Spiral) Parker, E. N., 1965, Planet. Space Sci., 13, 9
Fig.7 Trajectories of 2 particles - spherical TS Fig.8 Trajectories of 2 particles - blunt TS
●
magnitude ● Zhang, M. 1999, ApJ, 513, 409