Special Thanks to:
J. M. Albert, W. Li, S. K. Morley,
G. S. Cunningham, Y. Chen, R.
H. W. Friedel, G. D. Reeves, X. Li

Outline
• Introduction of Radiation Belt Dynamics:
Sources and Losses
• Advances in Quantitative RB Modeling:
Models and Inputs
• Challenges and Opportunities

Radiation Belt Dynamics
5
4
3
6
7
• Outer electron belt is very dynamic!
• The complex dynamics is a delicate balance of source, transport, and loss.
• Understanding the dynamics is the No.1 goal of the NASA Van Allen Probes Mission.
Van Allen Probes
(Aug 2012 - present)
10 4
2
93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09
Years
10 3
10 2
10 1
• Color-coded:
SAMPEX 2-6 MeV
Electron Flux (in log).
10 0
[Courtesy of Xinlin Li]

Radiation Belt Dynamics:
• External source: Inward radial transport due to interaction with ULF waves.
External Source ions electrons
Seed Populations
ULF waves
Internal Source
[Reeves et al., Science 2013]

Radiation Belt Dynamics:
• External source: Inward radial transport due to interaction with ULF waves.
• Internal source: Local acceleration due to interaction with VLF waves.
External Source
Magnetosonic waves
VLF chorus ions electrons
Seed Populations
Internal Source
[Reeves et al., Science 2013]

Radiation Belt Dynamics:
• Precipitation loss: pitch angle scattering by, e.g., VLF, EMIC waves.
EMIC waves hiss
VLF chorus ions electrons
Seed Populations

Radiation Belt Dynamics:
• Precipitation loss: pitch angle scattering by, e.g., VLF, EMIC waves.
• Magnetopause shadowing: outward radial transport ( ULF waves ) or magnetopause compression.
ions electrons
Seed Populations
ULF waves

Outline
• Introduction of Radiation Belt Dynamics:
Sources and Losses
• Advances in Quantitative RB Modeling:
Models and Inputs
• Challenges and Opportunities

Types of Radiation Belt Models
Inputs
Diffusion coefficients
Boundary conditions
Pros:
• Efficient, useful for global problems
[Courtesy of Yue Chen]
Outputs
PSD(µ,K,L,time)
Cons:
• Assumptions of quasilinear theory and diffusion physics

Types of Radiation Belt Models
• Fokker-Planck diffusion models
• Test particle codes
• PIC & Hybrid codes
Inputs
Diffusion coefficients
Global E&B models
Pros:
• Include drift phase and convection physics, useful for seed population
Outputs
PSD(E, α ,r, Φ ,time)
[Courtesy of V. Jordanova]
Cons:
• Assumptions of quasilinearity and diffusion; performance of the global E&B models

Types of Radiation Belt Models
• Fokker-Planck diffusion models
• Convection-Diffusion models
• PIC & Hybrid codes
Inputs
Global E&B models or
Analytical wave models
Pros:
• Include convection physics, no diffusion assumption
Outputs [Elkington et al., JASTP 2004] flux(E, α ,r, Φ ,time)
Cons:
• Performance of the global
E&B models (if MHD fields, no VLF waves); computationally expensive.

MHD Test Particle Simulation
Model flux
[Courtesy of F. Toffoletto]
• Trace electrons under global
LFM-RCM fields [Hudson et al., JGR 2015]
• Loss of MeV electrons by magnetopause shadowing and outward radial transport
(enhanced ULF waves)
450
350
250
25
15
5
10
0
-10
9
8
7
6
5
9
8
7
6
5
Magnetopause
-V x
(km/s)
P dyn
(nPa)
B z
(nT)
20:30 21:00
UT (hr) on Oct 8 2013
21:30
1.2 MeV
10 6
10 4
3.6 MeV
10 2
10 6
10 4
10 2

Test Quasi-Linear Theory
Quasi-Linear Diffusion Nonlinear Phase Bunching
Simulation Time
• Trace energetic electrons under a given wave model to test quasilinear theory and its limit .
• E.g., Tao [JGR 2012] found that for parallel propagating whistler waves, quasi-linear theory becomes invalid when the wave amplitude increases.
[Albert et al., GRL 2009]
Simulation Time
[Tao et al., JGR 2012]
0.1
B W
RMS
1.0
(nT)

Types of Radiation Belt Models
• Fokker-Planck diffusion models
• Convection-Diffusion models
• Test particle codes
Inputs
Initial plasma and field conditions
Outputs
Wave growth and interaction
[from LANL website]
Pros:
• Self-consistent wave particle interactions
Cons:
• Computationally expensive; limited coupling to global codes

Types of Radiation Belt Models
Selfconsistency
Global efficiency • Fokker-Planck diffusion models
• Convection-Diffusion models
• Test particle codes
• PIC & Hybrid codes
Inputs
Initial plasma and field conditions
Pros:
• Self-consistent wave particle interactions
Outputs
Wave growth and interaction
Cons:
• Computationally expensive; limited coupling to global codes

Fokker-Planck Diffusion Models
• 3D Fokker-Planck Equation [Schulz and Lanzerotti, 1974] :
• Simplified to 1D radial diffusion model at fixed µ and K:
− Useful when radial diffusion is the dominant process.
− Need reliable inputs for D
LL
, lifetime and source rate.

1D Radial Diffusion Model
• [Tu et al., JGR 2009]
• Goal: to reproduce the PSD dynamics observed at L=4 (with data-driven outer boundary at L=6)
• Empirical inputs: and

1D Radial Diffusion Model
• [Tu et al., JGR 2009]
• Goal: to reproduce the PSD dynamics observed at L=4 (with data-driven outer boundary at L=6)
• Empirical inputs: and
• Model results: well-reproduce the dynamics by all three different runs.
• Uncertainties in the model inputs: D
LL electron lifetime, and source rate
,

1D Radial Diffusion Model
• Z. Li et al. [JGR 2014] simulated the 1-month Van Allen Probes interval in March 2013 .
5
4
3
6
5
4
3
6
PSD: µ=1000 MeV/G K=0.01 G 1/2 Re
PSD data
RD model
• The 1 st enhancement at the beginning of March is reproduced by radial diffusion from a source at larger L .
• The Mar 17 storm enhancement is under-reproduced by radial diffusion only .
500
10
0
-10
01 Mar
V
SW
(km/s)
B z
(nT)
10 Mar
2013
20 Mar 30 Mar
10 -6
10 -8
10 -10
10 -6
10 -8
10 -10

2D Diffusion Model
• Coordinates
(µ,K,L)
(p, α ,L)
• Simplified to 2D momentum-pitch angle diffusion at fixed L
• Useful to model fast local acceleration and losses, when radial diffusion is not dominant.

2D Diffusion Model
• [W. Li et al., JGR 2007]: Applied a 2D diffusion model to study the acceleration and loss effects from different types of waves , located at different local times.
• Diffusion coefficients are calculated from static wave inputs specified for dayside/nightside chorus, EMIC, and hiss waves .

2D Diffusion Model
• Advance in model inputs:
– [Thorne et al., Nature 2013]
– Event-specific and global chorus wave model derived from POES proxy
– Ambient plasma density derived from in situ data
• Model well-reproduced the strong RB enhancement up to
7.2 MeV
10s keV precipitating electrons data
PSD vs time model
UT (hr) on Oct 8 2012 UT (hr) on Oct 8 2012
6 NOAA/POES chorus on equator

3D Diffusion Model
• Many different versions have been developed in the past 10 years:
– VERB (UCLA), DREAM3D (LANL), Dilbert? (Albert), REM (Rice), BAS model,
Salammb ȏ (French), STEERB (China) …
• Inputs: Diffusion Coefficients
Computational volume for 3D code
• Boundary Conditions :
α =0 PSD=0
α = π /2 dPSD/d α =0
L=1
L=L max
E=E max
E=E min
PSD=0 (atmosphere) outer boundary
PSD=0 seed population
(100 KeV)
α
E min boundary
L

3D Diffusion Model
• VERB results from Subbotin et al. [JGR 2011]
• Long-term simulation of the
CRRES interval to model the effects from different diffusion processes.
– Best reproduce the observations by including all the diffusion processes
• Wave and plasma inputs: dynamic but still empirical
(as a function of Kp).
Electron flux (E=1MeV, α =85 deg)
6
4
2
6
4
2
6
4
2
6
Data
RD + PAD
RD + PAD + ED
4
2 RD + PAD + ED + Mixed Diffusion
210 220 230 240 250 260 270 280 290 300
Day of Year 1990

3D Diffusion Model
• Need event-specific inputs for very strong events.
• [Tu et al., GRL 2014]: DREAM3D
– Model the strong enhancement during the Oct 2012 storm.
4
5
6 PSD data: µ=1279 MeV/G K=0.1 G 1/2 Re 10 -5
10 -6
10 -7
3
Oct 6 Oct 7 Oct 8
2012
Oct 9
10 -8
10 -9
Oct 10 Oct 11
Statistical chorus model
AE*<100nT 100<AE*<300nT AE*>300nT pT 2

3D Diffusion Model
• Need event-specific inputs for very strong events.
• [Tu et al., GRL 2014]: DREAM3D
– Model the strong enhancement during the Oct 2012 storm.
Statistical chorus model
AE*<100nT 100<AE*<300nT AE*>300nT pT 2
4
5
6 PSD data: µ=1279 MeV/G K=0.1 G 1/2 Re 10 -5
10 -6
10 -7
3
6
10 -8
10 -9
10 -5
10 -6
5
10 -7
4
3
With statistical waves
Oct 6 Oct 7 Oct 8
2012
Oct 9
10 -8
Oct 10 Oct 11
10 -9

3D Diffusion Model
• Need event-specific inputs for very strong events.
• [Tu et al., GRL 2014]: DREAM3D
– Model the strong enhancement during the Oct 2012 storm.
Statistical chorus model
AE*<100nT 100<AE*<300nT AE*>300nT pT 2
4
5
6 PSD data: µ=1279 MeV/G K=0.1 G 1/2 Re 10 -5
10 -6
10 -7
3
6
10 -8
10 -9
10 -5
10 -6
5
10 -7
4
10 -8
10 -9 3
1000
800
With statistical waves
600
400
200
0
Oct 6
AE (nT)
Oct 7 Oct 8
2012
Oct 9 Oct 10 Oct 11

3D Diffusion Model
• Need event-specific inputs for very strong events.
• [Tu et al., GRL 2014]: DREAM3D
– Model the strong enhancement during the Oct 2012 storm.
– Event-specific chorus waves
Event-specific chorus wave model
10s keV precipitating electrons chorus on equator
4
5
6 PSD data: µ=1279 MeV/G K=0.1 G 1/2 Re 10 -5
10 -6
10 -7
3
6
10 -8
10 -9
10 -5
10 -6
5
10 -7
4
10 -8
10 -9 3
1000
800
With statistical waves
600
400
200
0
Oct 6
AE (nT)
Oct 7 Oct 8
2012
Oct 9 Oct 10 Oct 11

3D Diffusion Model
• Need event-specific inputs for very strong events.
• [Tu et al., GRL 2014]: DREAM3D
– Model the strong enhancement during the Oct 2012 storm.
– Event-specific chorus waves
Event-specific chorus wave model
10s keV precipitating electrons chorus on equator
4
5
6 PSD data: µ=1279 MeV/G K=0.1 G 1/2 Re 10 -5
10 -6
10 -7
3
6
10 -8
10 -9
10 -5
10 -6
5
10 -7
4
10 -8
10 -9 3
1000
800
With real-time waves
600
400
200
0
Oct 6
AE (nT)
Oct 7 Oct 8
2012
Oct 9 Oct 10 Oct 11

3D Diffusion Model
• Need event-specific inputs for very strong events.
• [Tu et al., GRL 2014]: DREAM3D
– Model the strong enhancement during the Oct 2012 storm.
– Event-specific chorus waves
– Event-specific seed electrons
Event-specific seed population
10 8 electron flux data
10 6
10 4
4
5
6 PSD data: µ=1279 MeV/G K=0.1 G 1/2 Re 10 -5
10 -6
10 -7
3
6
10 -8
10 -9
10 -5
10 -6
5
10 -7
4
10 -8
10 -9 3
1000
800
With real-time waves
600
400
200
0
Oct 6
AE (nT)
Oct 7 Oct 8
2012
Oct 9 Oct 10 Oct 11
10 2
Oct 6
L * =4, α eq
=50 o
Oct 7 Oct 8
2012
Oct 9 Oct 10 Oct 11

3D Diffusion Model
• Need event-specific inputs for very strong events.
• [Tu et al., GRL 2014]: DREAM3D
– Model the strong enhancement during the Oct 2012 storm.
– Event-specific chorus waves
– Event-specific seed electrons
Event-specific seed population
10 8 electron flux data
10 6
10 4
4
5
6 PSD data: µ=1279 MeV/G K=0.1 G 1/2 Re 10 -5
10 -6
10 -7
3
6
10 -8
10 -9
10 -5
10 -6
5
10 -7
4
10 -8
10 -9 3
1000
800
600
400
200
0
Oct 6
AE (nT)
Oct 7 Oct 8
2012
Oct 9 Oct 10 Oct 11
10 2
Oct 6
L * =4, α eq
=50 o
Oct 7 Oct 8
2012
Oct 9 Oct 10 Oct 11

3D Model: Co-operative Physics
• Old: Is radial diffusion the dominant acceleration mechanism or local acceleration?
• New: How do RD, local heating, pitch angle scattering work together to produce the observed acceleration and loss of RB electrons?
4
5
6 PSD data: µ=1279 MeV/G K=0.1 G 1/2 Re 10 -5
10 -6
10 -7
3
Oct 6 Oct 7 Oct 8
2012
Oct 9
10 -8
10 -9
Oct 10 Oct 11

3D Model: Co-operative Physics
• Old: Is radial diffusion the dominant acceleration mechanism or local acceleration?
• New: How do RD, local heating, pitch angle scattering work together to produce the observed acceleration and loss of RB electrons?
4
5
6 PSD data: µ=1279 MeV/G K=0.1 G 1/2 Re 10 -5
10 -6
10 -7
3
6
5
10 -8
10 -9
10 -5
10 -6
10 -7
4
10 -8
3
Oct 6
RD only
Oct 7 Oct 8
2012
Oct 9 Oct 10 Oct 11
10 -9

3D Model: Co-operative Physics
• Old: Is radial diffusion the dominant acceleration mechanism or local acceleration?
• New: How do RD, local heating, pitch angle scattering work together to produce the observed acceleration and loss of RB electrons?
4
5
6 PSD data: µ=1279 MeV/G K=0.1 G 1/2 Re 10 -5
10 -6
10 -7
3
6
5
10 -8
10 -9
10 -5
10 -6
10 -7
4
10 -8
3
6
RD only
10 -9
10 -5
10 -6
5
10 -7
4
10 -8
3
Oct 6
RD + Chorus
Oct 7 Oct 8
2012
Oct 9 Oct 10 Oct 11
10 -9
• 3D model implies loss mechanisms: outward RD + precipitation

Advance in RB Models
• Great variety!
– Fokker-Planck diffusion models
– Convection-Diffusion models
– Test particles codes
– PIC & Hybrid codes
• Advances in modeling techniques
– E.g., 1D diffusion  2D diffusion  3D  4D
Van Allen Probes
• Advances in model inputs:
– E.g., chorus wave model:
Static  Dynamic but empirical  Event-specific
– Made possible by the extensive measurements from multiple missions!
NOAA POES

Outline
• Introduction of Radiation Belt Dynamics:
Sources and Losses
• Advances in Quantitative RB Modeling:
Models and Inputs
• Challenges and Opportunities

• Complex storm responses of RB electrons:
Increase
POLAR/HIST 1.2-2.4 MeV electron flux
50%
Decrease
20%
No change
30%
L
L L
Dst
1997
Dst
1999
Dst
1998
[Reeves et al., GRL 2003]

• Complex storm responses of RB electrons:
PSD: µ=1968 MeV/G K=0.1 G 1/2 Re
5.5
4.5
3.5
2.5
0
-20
-40
-60
-80
-100
Dst (nT)
Jul 4 Jul 6 Jul 8 Jul 10 Jul 12
2013
Jul 14 Jul 16 Jul 18
10 -6
10 -8
10 -10
Data
10 -12
Model

• Complex storm responses of RB electrons:
PSD: µ=1968 MeV/G K=0.1 G 1/2 Re
5.5
4.5
10 -6
3.5
10 -8
10 -10
Data
2.5
5.5
10 -12
10 -6
4.5
10 -8
3.5
10 -10
2.5
DREAM3D
Jul 4 Jul 6 Jul 8 Jul 10
2013
Jul 12 Jul 14 Jul 16 Jul 18
10 -12
Model
• Challenge: Can we model the complex storm variability and, more importantly, predict the various storm responses?
• Opportunities: Improve the model inputs & Include new physics.

• Current RB models are mature enough, but need better and more accurate model inputs.
• E.g., for diffusion-type models:
– Radial diffusion coefficient D
LL
D
LL
(Kp): 2 points
[Brautigam and Albert, JGR 2000]
Ground
GEO
D
LL
(Kp) [Ozeke et al., JGR 2012]
Multiple ground magnetometers
YORGML PINA ISLL GILL FCHU
10 1
10 0
Event-specific D
LL
Global ULF waves from:
Van Allen Probes
+
Ground magnetometers
+
Global MHD fields
10 -1
10 -2
10 -3
Still widely Used!
10 -4
2 3 7 8 4 5
L Shell
6

• Current RB models are mature enough, but need better and more accurate model inputs.
• E.g., for diffusion-type models:
– Radial diffusion coefficient D
LL
– Event-specific and global distribution of various waves
– Better plasma density and plasmapause models
– Reliable magnetic field models
Coupling between RB,
Ring Current, and
Plasmasphere

• Important to study new physics and quantify its importance .
• E.g., drift shell splitting  anomalous diffusion [O’Brien, GRL 2014]
• Effects of drift shell bifurcation
• Nonlinear, non-resonant wave particle interactions
Full diffusion tensor
Effects on RB electrons from REM model
Oct 2012 storm µ=2000 MeV/G
K=0.01 G 1/2 Re
Drift shell splitting
L( α ) [Zheng et al., GRL 2015]

• Focus Group of “ Quantitative Assessment of Radiation Belt
Modeling ” (2014-2018)
• Co-chairs: Jay Albert, Wen Li, Steve Morley, Weichao Tu
• Goals:
– Bring together the current state-of-the-art RB models and new physics.
– Develop event-specific and global RB model inputs (waves, plasma, seed population, magnetic fields).
– Combine all these components to achieve a quantitative assessment of the RB modeling by validating against real-time measurements.
• Activities:
– A review of current RB models and required inputs (last year).
– “RB buildup” and “RB dropout” Challenges (starting this year).
– Joint activities with other FGs.

Donut time?
• Radiation belt is a very dynamic and complicated system due to the delicate balance between source, transport, and loss.
• Great progress has been made in quantitative modeling of radiation belt dynamics:
– Advances in state-of-the-art models
– Advances in model inputs
• Challenges on reproducing the complex storm responses, improving model inputs, and exploring new physics.