IMAGE EUV & RPI Derived Distributions of Plasmaspheric Plasma and Plasmaspheric Modeling

IMAGE EUV & RPI Derived Distributions of Plasmaspheric Plasma and Plasmaspheric Modeling D. Gallagher, M. Adrian, J. Green, C. Gurgiolo, G. Khazanov, A. King, M. Liemohn, T. Newman, J. Perez, J. Taylor, B. Sandel

Image Analysis Techniques • Iterative Gurgiolo Approximation • Arbitrary plasma density distribution • One flux tube assumed to dominate each pixel • Custom hand analysis • Genetic Algorithm • Parameterized function • Arbitrary plasma density distribution • Single Image Tomography • With or without a priori assumption for plasma distribution along Earth’s magnetic field lines • Single equatorial location contributes to multiple pixels in instrument image, i.e. “multiple perspective” Yosemite 2002: Magnetospheric Imaging

One Kind of Hand Analysis • Identify feature • Trace boundaries • Estimate density structure, simulate image, and compare Yosemite 2002: Magnetospheric Imaging

Channel Matches as Observed,but Outer Plasmaspheric Densities too High Yosemite 2002: Magnetospheric Imaging

Exponential Decrease with L-Shell OutsideChannel Approximates Observation Yosemite 2002: Magnetospheric Imaging

Same Approach Can be UsedGenerally On an Event Basis Yosemite 2002: Magnetospheric Imaging

In this Case, ModelResults WorkFairly Well Yosemite 2002: Magnetospheric Imaging

RPI Inversion for June 10, 2001 Yosemite 2002: Magnetospheric Imaging

Guided & Direct Echoes @ 02:38:57 Guided echo trace from local hemisphere Direct echo trace from local hemisphere Yosemite 2002: Magnetospheric Imaging

RPI Derived Field Aligned Density Distributions Yosemite 2002: Magnetospheric Imaging

Inversion of EUV Images Yosemite 2002: Magnetospheric Imaging

Genetic Algorithm:Development and Application of Impulse Response Matrix • Description of Problem • Development of Impulse Response Matrix • Matrix Inversion Method • Genetic Algorithm Approach Yosemite 2002: Magnetospheric Imaging

Impulse Matrix The Response (or Effect) of each L Shell will be Different This Diagram Suggests that for a Given Satellite Position and Look Direction, there is a Function that Relates the Density Along the x-axis to the LOS Integration. Crossing a Particular L Shell. Yosemite 2002: Magnetospheric Imaging

Impulse Response Matrix • Digital signal processing deconvolution techniques work using the impulse response of the system. • In this situation the impulse response for each pixel is different, there is not a system impulse response, standard deconvolution techniques cannot be used. • However, there is a specific impulse response for each pixel, this suggests an Impulse Response Matrix. • x = density along x-axis; b = LOS integration at camera location; A = Impulse Response Matrix. Ax = b. Yosemite 2002: Magnetospheric Imaging

5 xLmax = 9R Grid spacing = 1R # of Grid points = 9 4 3 2 1 0 -1 -2 1 2 3 4 5 6 7 8 9 Impulse Matrix Inversion A is not necessarily symmetric. If bis known then xcan be obtained from x = b[At(A At)-1] xLmax = 9R Non-uniform grid spacing # of Grid points = 18 4 3 2 1 0 -1 -2 1 2 3 4 5 6 7 8 9 Yosemite 2002: Magnetospheric Imaging

Genetic Algorithm Approach • The genetic algorithm approach works by randomly “guessing” solutions, comparing them to the satellite image, selecting the best solutions, using those to generate more solutions, then testing them etc.. • The genetic algorithm approach is now be feasible since density distributions x can be “guessed”, then tested using Ax=b. (The method was not feasible before because for each x “guessed” an entire LOS integration was necessary, now only a matrix multiplication is necessary.) Yosemite 2002: Magnetospheric Imaging

Genetic Algorithm Approach Applied to 2D Problem • 300 solutions (density at 18 grid locations along x-axis) were randomly generated. • The solutions were transferred and compared to the LOS integration. • The top 50 solutions were used as “parents” to generate a new set of 300 solutions. The parents for each solution were randomly chosen with “best” solutions having a higher likelihood of being chosen. • The location where the two parents joined to form the new solution was randomly chosen. • Each new solution had a 50-50 chance of having values mutated. Yosemite 2002: Magnetospheric Imaging

Genetic Algorithm Results iter=2 iter=2 t=0.66s t=0.66s x-axis density LOS integration iter=25 iter=25 t=5.49s t=5.49s Yosemite 2002: Magnetospheric Imaging

Genetic Algorithm Results iter=50 iter=50 t=10.60s t=10.60s x-axis density LOS integration iter=100 iter=100 t=20.71s t=20.71s Yosemite 2002: Magnetospheric Imaging

Genetic Algorithm Results forEUV Image from August 11, 2001 1422UT Yosemite 2002: Magnetospheric Imaging

Tomographic Algebraic Reconstruction Technique (ART) • Volume Reconstruction • Back-projection • Methodology: • 1. Build 3D Grid • 2. Trace Pixel Beams through Grid • a. Find Sampled Voxels • 3. Construct Integration (Summation) Formulae • 4. Solve Formulae -> Generate Density Volume Yosemite 2002: Magnetospheric Imaging

0 10 0 P1 P2 7 Reconstruction: Outline V(P1) = a1V2,0 + a2V2,1 + a3V3,2 + … + a10V3,10 Solve: Yosemite 2002: Magnetospheric Imaging

Let’s Get Back to May 24, 2000and Reduced Plasma in Outer PS IMAGE ENA and EUV Observations Yosemite 2002: Magnetospheric Imaging

What Does Physical Modeling Show? Yosemite 2002: Magnetospheric Imaging

HENA EUV RC Yosemite 2002: Magnetospheric Imaging

Where is PS IMAGE Inversion Leading? • Comparison of physical models of PS, RC, & RB relative to mutual interactions between populations and model advancement  GEM • Study of PS refilling across all LT & L • Derivation of subauroral electric fields through feature tracking • A new breed of PS statistical modeling Yosemite 2002: Magnetospheric Imaging

IMAGE EUV & RPI Derived Distributions of Plasmaspheric Plasma and Plasmaspheric Modeling