1. Preferential Low-Latitude Source and Transport of Low-Energy Anomalous Cosmic Rays
Please contact me at
Matthew E. Hill
Johns Hopkins University Applied Physics Laboratory +
Additional Brief Topics Inspired by Yesterday's Discussions
A. Jovian Magnetotail (related to parallel vs. perpendicular diffusion, Dröge)
B. Interplanetary Suprathermal Ions (related to radial dependence of PUI/ST, Fahr)
C. The v-5 spectrum (comment on ISSI conference by Fahr).
D. Ions upstream of the TS (magnetic orientation and particle acceleration at TS, leRoux)
E. Recent Low-Energy Ion Measurements from the Heliosheath (general discussion)
Items C, D, and E are preliminary, please contact me.
International Workshop: New Perspectives on Cosmic Rays in the Heliosphere
Stonehenge, Parys, The Free State, South Africa  23 March 2010
Hosted by the Unit for Space Physics  North-West University

2. Preferential Low-Latitude Source and Transport of Low-Energy Anomalous Cosmic Rays
Please contact me at
Matthew E. Hill
Johns Hopkins University Applied Physics Laboratory
Look at these First +
Additional Brief Topics Inspired by Yesterday's Discussions
A. Jovian Magnetotail (related to parallel vs. perpendicular diffusion, Dröge)
B. Interplanetary Suprathermal Ions (related to radial dependence of PUI/ST, Fahr)
C. The v-5 spectrum (comment on ISSI conference by Fahr).
D. Ions upstream of the TS (magnetic orientation and particle acceleration at TS, leRoux)
E. Recent Low-Energy Ion Measurements from the Heliosheath (general discussion)
Items C, D, and E are preliminary, please contact me.
International Workshop: New Perspectives on Cosmic Rays in the Heliosphere
Stonehenge, Parys, The Free State, South Africa  23 March 2010
Hosted by the Unit for Space Physics  North-West University

3. Preferential Low-Latitude Source and Transport of Low-Energy Anomalous Cosmic Rays
Please contact me at
Matthew E. Hill
Johns Hopkins University Applied Physics Laboratory
Look at these First +
Additional Brief Topics Inspired by Yesterday's Discussions
A. Jovian Magnetotail (related to parallel vs. perpendicular diffusion, Dröge)
B. Interplanetary Suprathermal Ions (related to radial dependence of PUI/ST, Fahr)
C. The v-5 spectrum (comment on ISSI conference by Fahr).
D. Ions upstream of the TS (magnetic orientation and particle acceleration at TS, leRoux)
E. Recent Low-Energy Ion Measurements from the Heliosheath (general discussion)
Items C, D, and E are preliminary, please contact me.
International Workshop: New Perspectives on Cosmic Rays in the Heliosphere
Stonehenge, Parys, The Free State, South Africa  23 March 2010
Hosted by the Unit for Space Physics  North-West University

4. Speed (1/v scale) vs. Day of 2007
Energetic Particle Injections in the Jovian Magnetotail NH/PEPSSI keV/nuc ions
30 days per panel from DOY
2 of 4 panels shown
600 to 1900 RJ
Speed (1/v scale) vs. Day of 2007
Hill et al., 2009 JGR

5. Hill et al., 2009 JGR

6. Illustration of scenario consistent with all known observations
Particle travel through and fill empty flux tubes (magnetic filaments), that are well-connected to near-Jupiter region. NH observes these particles as it passes between adjacent tubes. The timing of the transitions and re-entering of tubes indicates the scale of these structures ~5 RJ.
Hill et al., 2009 JGR

7. Preferential Low-Latitude Source and Transport of Low-Energy Anomalous Cosmic Rays
Please contact me at
Matthew E. Hill
Johns Hopkins University Applied Physics Laboratory
Look at these First +
Additional Brief Topics Inspired by Yesterday's Discussions
A. Jovian Magnetotail (related to parallel vs. perpendicular diffusion, Dröge)
B. Interplanetary Suprathermal Ions (related to radial dependence of PUI/ST, Fahr)
C. The v-5 spectrum (comment on ISSI conference by Fahr).
D. Ions upstream of the TS (magnetic orientation and particle acceleration at TS, leRoux)
E. Recent Low-Energy Ion Measurements from the Heliosheath (general discussion)
Items C, D, and E are preliminary, please contact me.
International Workshop: New Perspectives on Cosmic Rays in the Heliosphere
Stonehenge, Parys, The Free State, South Africa  23 March 2010
Hosted by the Unit for Space Physics  North-West University

8. Example Quiet Time H+, He+, and He++ Spectra
We focus on the 41.7 keV/nuc ions here
Quiet Times
Only includes “quiet time” but no qualitative results change when active times added.
We used protons to identify quiet times. We also did an alternate quiet time selection with no qualitative change.
All 3 species have ST tails. H+ and He++ consistent with F&G, not He+
Hill et al ApJL

9. There is a 3-order-of-magnitude disagreement!!
From 1 to 9 AU Simulated He+ DECREASES by factor of 13
From 1 to 9 AU Measured He+ INCREASES by factor of 67
There is a 3-order-of-magnitude disagreement!!
Hill et al ApJL

10. Preferential Low-Latitude Source and Transport of Low-Energy Anomalous Cosmic Rays
Matthew E. Hill
Johns Hopkins University Applied Physics Laboratory
Now for the main topic +
Additional Brief Topics Inspired by Yesterday's Discussions
A. Jovian Magnetotail (related to parallel vs. perpendicular diffusion, Dröge)
B. Interplanetary Suprathermal Ions (related to radial dependence of PUI/ST, Fahr)
C. The v-5 spectrum (comment on ISSI conference by Fahr).
D. Ions upstream of the TS (magnetic orientation and particle acceleration at TS, leRoux)
E. Recent Low-Energy Ion Measurements from the Heliosheath (general discussion)
Items C, D, and E are preliminary, please contact me.
International Workshop: New Perspectives on Cosmic Rays in the Heliosphere
Stonehenge, Parys, The Free State, South Africa  23 March 2010
Hosted by the Unit for Space Physics  North-West University

11. Approaches to Studying ACR Transport
Method 1. Observations – Quasi-Local Gradients
Once the heliosphere reached a quasi-steady state the residual variations seen at V1 and V2 are all spatial. This allows the use of a non-standard gradient determination that provides both latitudinal and radial gradients simultaneously. Each species/energy is analyzed separately.
PRO: Data-based. Model-independent.
CON: The analysis method is not standard. No time dependence.
Method 2. Phenomenology – Simultaneous Fits
A single equation is used to simultaneously fit all the V1/V2 ACR data. The equation is ad hoc but motivated by physics.
PRO: Simultaneous fit means energy, radial, latitudinal, and temporal dependence included.
CON: A lot of parameters and model is ad hoc.
Method 3. Modeling – Solve CR Transport Equation
The Parker cosmic ray transport equation (Fokker-Planck) is solved numerically in the time-dependent, energy-dependent, spherically symmetric case.
PRO: Standard equation/analysis. Physics-based.
CON: Can only get radius, time, and energy (no latitude information)
Method 4. Theory – Global Curvature-Gradient Drifts
Drift velocity components are calculated for a Parker spiral, flat current sheet geometry and compared to the radial convective velocity for particles of different rigidities.
PRO: Standard theory, well-understood.
CON: Assumptions are simple. No data.

12. Look back at the 1992-1999 A > 0 Recovery Period
Positions in ~1996.
Look back at the A > 0 Recovery Period
Hill, 2001

13. Long-term ACR intensity profiles and spectra during the A>0 recovery period at Voyager 1&2 and 1 AU. At V1/V2 temporal variations dominate from , then spatial gradients from
spatial
Temporal
Hill et al, 2002 ApJL
spatial
Temporal
Hill et al, 2003 JGR

14. Approaches to Studying ACR Transport
Method 1. Observations – Quasi-Local Gradients
Once the heliosphere reached a quasi-steady state the residual variations seen at V1 and V2 are all spatial. This allows the use of a non-standard gradient determination that provides both latitudinal and radial gradients simultaneously. Each species/energy is analyzed separately.
PRO: Data-based. Model-independent.
CON: The analysis method is not standard. No time dependence.
Method 2. Phenomenology – Simultaneous Fits
A single equation is used to simultaneously fit all the V1/V2 ACR data. The equation is ad hoc but motivated by physics.
PRO: Simultaneous fit means energy, radial, latitudinal, and temporal dependence included.
CON: A lot of parameters and model is ad hoc.
Method 3. Modeling – Solve CR Transport Equation
The Parker cosmic ray transport equation (Fokker-Planck) is solved numerically in the time-dependent, energy-dependent, spherically symmetric case.
PRO: Standard equation/analysis. Physics-based.
CON: Can only get radius, time, and energy (no latitude information)
Method 4. Theory – Global Curvature-Gradient Drifts
Drift velocity components are calculated for a Parker spiral, flat current sheet geometry and compared to the radial convective velocity for particles of different rigidities.
PRO: Standard theory, well-understood.
CON: Assumptions are simple. No data.

15. Standard Non-Local Gradient
(e.g., used by McDonald or Cummings for GCRs and ACRs)
Need THREE spacecraft to get TWO gradients.
Forced to assume longitudinal symmetry to use V1, V2, P10
The standard method of calculating ACR spatial intensity gradients using three widely spaced spacecraft relies on the poor assumption of longitudinal symmetry.
We need another way.

16. Quasi-Local Gradient Method
a new technique that takes advantage of the location of the Voyagers and the state of the heliosphere
QLG method relies on better assumption of a quasi-steady state and uses both s/c near the nose.
Hill and Hamilton, 2003
Quasi-Local Gradient
for comparison:
Standard Non-Local Gradient

17. y Quasi-Local Gradient Method
a new technique that takes advantage of the location of the Voyagers and the state of the heliosphere
QLG method relies on better assumption of a quasi-steady state and uses both s/c near the nose. y
Hill and Hamilton, 2003
Quasi-Local Gradient
for comparison:
Standard Non-Local Gradient

18. y vs. x Quasi-Local Gradient Method
a new technique that takes advantage of the location of the Voyagers and the state of the heliosphere
QLG method relies on better assumption of a quasi-steady state and uses both s/c near the nose.
y vs. x
Hill and Hamilton, 2003
Quasi-Local Gradient
for comparison:
Standard Non-Local Gradient

19. y vs. x y = gr + xgl Quasi-Local Gradient Method
a new technique that takes advantage of the location of the Voyagers and the state of the heliosphere
QLG method relies on better assumption of a quasi-steady state and uses both s/c near the nose.
y vs. x
y = gr + xgl
Hill and Hamilton, 2003
Quasi-Local Gradient
for comparison:
Standard Non-Local Gradient

20. Quasi-Local Gradient Method
Fit to data: all possible intensity pairs
This is carried out separately for each species and energy band. This example is “high energy” oxygen.
Hill and Hamilton, 2003

21. Approaches to Studying ACR Transport
Method 1. Observations – Quasi-Local Gradients
Once the heliosphere reached a quasi-steady state the residual variations seen at V1 and V2 are all spatial. This allows the use of a non-standard gradient determination that provides both latitudinal and radial gradients simultaneously. Each species/energy is analyzed separately.
PRO: Data-based. Model-independent.
CON: The analysis method is not standard. No time dependence.
Method 2. Phenomenology – Simultaneous Fits
A single equation is used to simultaneously fit all the V1/V2 ACR data. The equation is ad hoc but motivated by physics.
PRO: Simultaneous fit means energy, radial, latitudinal, and temporal dependence included.
CON: A lot of parameters and model is ad hoc.
Method 3. Modeling – Solve CR Transport Equation
The Parker cosmic ray transport equation (Fokker-Planck) is solved numerically in the time-dependent, energy-dependent, spherically symmetric case.
PRO: Standard equation/analysis. Physics-based.
CON: Can only get radius, time, and energy (no latitude information)
Method 4. Theory – Global Curvature-Gradient Drifts
Drift velocity components are calculated for a Parker spiral, flat current sheet geometry and compared to the radial convective velocity for particles of different rigidities.
PRO: Standard theory, well-understood.
CON: Assumptions are simple. No data.

22. h(t,R) Phenomenological Modeling of ACR Motivation Definitions
Hill, 2001
Phenomenological Fit Function
14 time series / 18 parameters = 7 scale factors JSi + 11 dynamical parameters
rS gr∞ glo D to to , a1 = TS radius, gradients, time parameters (g1 g2 g4 g5) = rigidity parameters
Note this is a fit to ALL the data simultaneously, not curve by curve.
Comparison
To parameterize the time series independently need 3 parameters per series for a total of 42 parameters. Remove scaling and get 28 parameters compared to 11.

23. h(t,R) Phenomenological Modeling of ACR Motivation Definitions
Number of fit parameters reduced from 42 (14 scaling and 28 dynamical) parameters to 18 (7 scaling and 11 dynamical) parameters, compared to parametrizing each curve and, most importantly, all 14 time series are now linked together and fit simultaneously using a physically-motivated function.
Motivation
Definitions
h(t,R)
Hill, 2001
Phenomenological Fit Function
14 time series / 18 parameters = 7 scale factors JSi + 11 dynamical parameters
rS gr∞ glo D to to , a1 = TS radius, gradients, time parameters (g1 g2 g4 g5) = rigidity parameters
Note this is a fit to ALL the data simultaneously, not curve by curve.
Comparison
To parameterize the time series independently need 3 parameters per series for a total of 42 parameters. Remove scaling and get 28 parameters compared to 11.

24. One function j(r,l,t,R) fits all data simultaneously, so we can now examine the model intensity at any HG – radius, or latitude, time, or rigidity, not just where the Voyagers are.
Intensity vs. time (years)
Hill, 2001

25. Source is at low latitudes
Pole
Example ions:
20 MeV H+ or 5 MeV/nuc He+
Source is at low latitudes
Equator
Hill, 2001

26. Source is at low latitudes
Pole
Example ions:
25 MeV/nuc He+ or 1 MeV/nuc O+
Source is at low latitudes
Equator
Hill, 2001

27. Pole
Example ion:
25 MeV/nuc O+
Equator
Hill, 2001

28. Approaches to Studying ACR Transport
Method 1. Observations – Quasi-Local Gradients
Once the heliosphere reached a quasi-steady state the residual variations seen at V1 and V2 are all spatial. This allows the use of a non-standard gradient determination that provides both latitudinal and radial gradients simultaneously. Each species/energy is analyzed separately.
PRO: Data-based. Model-independent.
CON: The analysis method is not standard. No time dependence.
Method 2. Phenomenology – Simultaneous Fits
A single equation is used to simultaneously fit all the V1/V2 ACR data. The equation is ad hoc but motivated by physics.
PRO: Simultaneous fit means energy, radial, latitudinal, and temporal dependence included.
CON: A lot of parameters and model is ad hoc.
Method 3. Modeling – Solve CR Transport Equation
The Parker cosmic ray transport equation (Fokker-Planck) is solved numerically in the time-dependent, energy-dependent, spherically symmetric case.
PRO: Standard equation/analysis. Physics-based.
CON: Can only get radius, time, and energy (no latitude information)
Method 4. Theory – Global Curvature-Gradient Drifts
Drift velocity components are calculated for a Parker spiral, flat current sheet geometry and compared to the radial convective velocity for particles of different rigidities.
PRO: Standard theory, well-understood.
CON: Assumptions are simple. No data.

29. Numerical modeling of the Parker Cosmic Ray Transport Equation
Retain, radius, energy, and time. Start with empty heliosphere and treat the source as a boundary condition. Only three parameters: diffusion coefficient, source position, and power law index of source spectrum. Vsw was fixed.
Rewrote Fokker-Planck for the spherically symmetric case to study the simultaneous radial, temporal, and energy dependence of ACR transport.
Solved the following general PDE numerically using a finite differencing scheme. Operator splitting: Crank-Nicholson and explicit forward differencing. Lax method option included. Tested against analytical solutions and limiting cases. The coefficients can vary on x, y, or t.
Hill, 2001

30. Intensity vs. Energy/nuc Intensity vs. year
1992
1994
1998
ACR Oxygen
1-4 MeV/nuc
7-20 MeV/nuc
20-40 MeV/nuc
As was mentioned yesterday by Adri Burger, it is “easy to fit one set of data; we need to fit simultaneous observations”
Very good fit (given the limitations). The discrepancies are understandable due to measured latitudinal variations (which are not modeled here).
Here we fit spectra and time profiles at three widely separated spacecraft using a minimum of parameters
Hill, 2001

31. Approaches to Studying ACR Transport
Method 1. Observations – Quasi-Local Gradients
Once the heliosphere reached a quasi-steady state the residual variations seen at V1 and V2 are all spatial. This allows the use of a non-standard gradient determination that provides both latitudinal and radial gradients simultaneously. Each species/energy is analyzed separately.
PRO: Data-based. Model-independent.
CON: The analysis method is not standard. No time dependence.
Method 2. Phenomenology – Simultaneous Fits
A single equation is used to simultaneously fit all the V1/V2 ACR data. The equation is ad hoc but motivated by physics.
PRO: Simultaneous fit means energy, radial, latitudinal, and temporal dependence included.
CON: A lot of parameters and model is ad hoc.
Method 3. Modeling – Solve CR Transport Equation
The Parker cosmic ray transport equation (Fokker-Planck) is solved numerically in the time-dependent, energy-dependent, spherically symmetric case.
PRO: Standard equation/analysis. Physics-based.
CON: Can only get radius, time, and energy (no latitude information)
Method 4. Theory – Global Curvature-Gradient Drifts
Drift velocity components are calculated for a Parker spiral, flat current sheet geometry and compared to the radial convective velocity for particles of different rigidities.
PRO: Standard theory, well-understood.
CON: Assumptions are simple. No data.

32. For all but the highest rigidity (e. g
For all but the highest rigidity (e.g., 25+ MeV/nuc Oxygen) drifts are not important for ACRs.
We should not let the well-engrained drift patterns misguide our interpretation of ACRs
Hill, 2004

33. The Radial Gradients from the QLG method, Phenomenological fit, and numerical model all agree within uncertainties for three species spaning a factor of 30 in rigidity
The Latitudinal Gradients from the QLG method and Phenomenological fit agree just as well. The drift speed comparison illustrates when drifts should be important.
Since (1) we know drifts are not important and yet there are (2) large negative latitudinal gradients and (3) large positive radial gradients, this tells us that the source is (a) beyond the Voyagers and (b) at low latitudes.
Hill and Hamilton, 2003

34. Summary of Main ACR Low-Latitude Topic
Experimental Result: For all but the highest rigidity ACRs (R > 2GV) the important transport activity is dominantly at low latitudes during both polarities of the solar cycle. Drifts are not important for these ACRs.
Since (1) we know drifts are not important and yet there are (2) large negative latitudinal gradients and (3) large positive radial gradients, this tells us that the source is (a) beyond the Voyagers and (b) at low latitudes.

35. Summary of Brief Topics
Jovian Magnetotail (related to parallel vs. perpendicular diffusion, Dröge)
New Horizons PEPSSI data show drop outs/steps due to flux tube crossing
B. Interplanetary Suprathermal Ions (related to radial dependence of PUI/ST, Fahr)
Accelerated pickup ion intensities increase as function of distance, unexpected.
C. The v-5 spectrum at Cassini (comment on ISSI conference by Fahr).
There is a clear preference for the v-5 spectrum for H+, and He++, less so for He+
D. Ions upstream of the TS (magnetic orientation and particle accel. at TS, leRoux)
The ion anisotropies are organized by speed and the spectra by total energy.
E. Recent Low-Energy Ion Measurements from the Heliosheath (general discussion)
Low energy ions (20 keV-4 MeV) very similar at V1 and V2 and steady, ACRs unfold
Items C, D, and E are preliminary, please contact me.

36. References for low-latitude ACR topic
Hill, M.E., Transport Phenomena of Anomalous Cosmic Rays During the Recovery Phase of Solar Cycle 22, Ph.D. Dissertation, University of Maryland, December 2001.
Hill, M.E., D.C. Hamilton, and S.M. Krimigis, Evolution of Anomalous Cosmic-Ray Oxygen and Helium Energy Spectra During the Solar Cycle 22 Recovery Phase in the Outer Heliosphere, Astrophys. J. 572, L169-L172, 2002.
Hill, M.E, and D.C. Hamilton, Quasi-Local and Non-Local Intensity Gradients of Anomalous Cosmic Rays, Proc. 28th Int. Cosmic Ray Conf, 7, , 2003
Hill, M.E., D.C. Hamilton, J.E. Mazur, and S.M. Krimigis, Anomalous cosmic ray intensity variations in the inner and outer heliosphere during the solar cycle 22 recovery phase (1991–1999), J. Geophys. Res. 108, 8037, doi: /2003JA009914, 2003.
Hill, M.E., Investigating the Heliosphere with Low Energy Anomalous Cosmic Rays, in Physics of the Outer Heliosphere: Third International Astrophysics Conference/IGPP, V. Florinski, N.V. Pogorelov, and G.P. Zank, eds., American Institute of Physics, CP719, , 2004.
References for “Brief Topics”
Hill, M.E. et al., Interplanetary suprathermal He+ and He++ Observations during Quiet Periods From 1 to 9 AU and Implications for Particle Acceleration, Astrophys. J. 699, L26-L30, 2009.
Hill, M.E., et al., Energetic particle evidence for magnetic filaments in Jupiter’s magnetotail, J. Geophys. Res. 114, A11201, doi: /2009JA014374, 2009.