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

February 6, 2001Yosemite 2002: Magnetospheric Imaging 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”

February 6, 2001Yosemite 2002: Magnetospheric Imaging One Kind of Hand Analysis Identify feature Trace boundaries Estimate density structure, simulate image, and compare

February 6, 2001Yosemite 2002: Magnetospheric Imaging Channel Matches as Observed, but Outer Plasmaspheric Densities too High

February 6, 2001Yosemite 2002: Magnetospheric Imaging Exponential Decrease with L-Shell Outside Channel Approximates Observation

February 6, 2001Yosemite 2002: Magnetospheric Imaging Same Approach Can be Used Generally On an Event Basis

February 6, 2001Yosemite 2002: Magnetospheric Imaging In this Case, Model Results Work Fairly Well

February 6, 2001Yosemite 2002: Magnetospheric Imaging RPI Inversion for June 10, 2001

February 6, 2001Yosemite 2002: Magnetospheric Imaging Guided & Direct 02:38:57 Guided echo trace from local hemisphere Direct echo trace from local hemisphere

February 6, 2001Yosemite 2002: Magnetospheric Imaging Guided & Direct 02:52:57 Guided echo trace from local hemisphere Direct echo trace from local hemisphere

February 6, 2001Yosemite 2002: Magnetospheric Imaging Guided & Direct 02:54:56 Guided echo trace from local hemisphere Direct echo trace from local hemisphere

February 6, 2001Yosemite 2002: Magnetospheric Imaging RPI Derived Field Aligned Density Distributions

February 6, 2001Yosemite 2002: Magnetospheric Imaging Inversion of EUV Images

February 6, 2001Yosemite 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

February 6, 2001Yosemite 2002: Magnetospheric Imaging Crossing a Particular L Shell. 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. The Response (or Effect) of each L Shell will be Different Impulse Matrix

February 6, 2001Yosemite 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.

February 6, 2001Yosemite 2002: Magnetospheric Imaging Impulse Matrix Inversion A is not necessarily symmetric. If b is known then x can be obtained from x = b[A t (A A t ) -1 ] xLmax = 9R Non-uniform grid spacing # of Grid points = 18

February 6, 2001Yosemite 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.)

February 6, 2001Yosemite 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 chance of having values mutated.

February 6, 2001Yosemite 2002: Magnetospheric Imaging Genetic Algorithm Results iter=25 t=5.49s iter=25 t=5.49s iter=2 t=0.66s LOS integration t=0.66s x-axis density iter=2

February 6, 2001Yosemite 2002: Magnetospheric Imaging Genetic Algorithm Results iter=50 iter=100 t=10.60s t=20.71s iter=50 t=10.60s iter=100 t=20.71s LOS integrationx-axis density

February 6, 2001Yosemite 2002: Magnetospheric Imaging Genetic Algorithm Results for EUV Image from August 11, UT

February 6, 2001Yosemite 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

February 6, 2001Yosemite 2002: Magnetospheric Imaging Reconstruction: Outline P1 P2 V(P1) = a 1 V 2,0 + a 2 V 2,1 + a 3 V 3,2 + … + a 10 V 3,10 Solve:

February 6, 2001Yosemite 2002: Magnetospheric Imaging Let’s Get Back to May 24, 2000 and Reduced Plasma in Outer PS IMAGE ENA and EUV Observations

February 6, 2001Yosemite 2002: Magnetospheric Imaging What Does Physical Modeling Show?

February 6, 2001Yosemite 2002: Magnetospheric Imaging HENAEUV RC

February 6, 2001Yosemite 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