Stuart D. Bale, Ryan J. Prenger, and Forrest S. Mozer

1. 102 ‘timing’ normals in X-Y and X-Z GSE planes, overplotted with a parabolic shock model (Filbert and Kellogg, 1979), with no pressure scaling. By eye, the typical normal is surprisingly well aligned with the model, suggesting a lack of dynamic structure. BN from the timing normal. The angle between the ‘timing normal’ and the maximum variance normal. Shock speed, in the spacecraft frame, as determined by the timing analysis. The Recipe • Apply FIR filter to SCP and electric fields • Cross-correlate SCP pairs for time shifts dtij • Calculate ‘timing’ normal and shock speed from • x12 y12 z12 dt12 • x13 y13 z13 · n = v dt13 • x14 y14 z14 dt14 • Fit for shock ramp scale (hyperbolic tangent) • Boost E to shock frame by (vsh x B) • Calculate Maximum Variance normal • Rotate to Maximum Variance system • Calculate Normal Incidence Frame (NIF) • velocity vNIF = n x (vsw x n) and • boost E by (vNIF x B) to NIF frame • Integrate normal electric field in NIF frame • for NIF potential Shock ramp scale (km) from the hyperbolic tangent fit. Shock ramp scale (c/wpi) from the hyperbolic tangent fit. SW density is estimated from the spacecraft potential. We use spacecraft potential as a proxy for electron density. Spacecraft potential is measured at 5 s/s in normal mode (approximately 25X the cadence of the particle measurements). The spacecraft potential measurement is subject to contamination at harmonics of the spin frequency (0.25 Hz). We use a non-recursive (FIR) filter to notch the signal at these frequencies, which introduce a phase error near the notch frequencies. Electric field, electric potential, and ‘density’ measurements at quasi-perpendicular collisionless shocks: Cluster/EFW measurements Spacecraft potential is transformed, using coefficients from a fit between CIS plasma density moments and EFW spacecraft potential. This new 'density' parameter is then fitted by a function n(x) = n0 + n1 tanh(k (x-x0)) and the 'ramp' is identified as the scale L = |n|/|dn/dx| at x0. In the two panels above, the fitted density ramp is at top. The middle panel is the density with the hyperbolic tangent subtracted, and the lower panel is the wavelet spectrum of the difference signal. Although not shown here, much of this structure appears to be time-stationary and hence may be fine-scale density structure on the ramp. spacecraft potential 4 s/c XCF NIF electric potential electric field (NIF/MV) ET const spacecraft potential 4 s/c, shifted to SC1 time electric field (MV) vector electric field (E·B = 0) electric field magnitude (E·B = 0) solar wind spacecraft potential 4 s/c on spatial scale vsw (CIS) shocks electric field magnitude electric field (GSE) Stuart D. Bale, Ryan J. Prenger, and Forrest S. Mozer Space Sciences Laboratory, University of California, Berkeley …with particular thanks to Jim McFadden and the Cluster CIS and FGM teams spacecraft potential Spacecraft potential is locally higher (more negative) in the less dense solar wind 2001-03-31 19:45 shock spacecraft potential (V) XCF NIF electric potential electric field (NIF/MV) ET const s/c potential electric field (MV) spacecraft potential 4 s/c vsw (CIS) s/c potential w/ FIR filter s/c potential w/ filter s/c potential w/ filter • …some conclusions • shocks speeds: 10 km/s • shock normals: like model? • shock ramp scale: c/wpi • NIF potentials: 700-2000 V • dHT frame is difficult electric field magnitude spacecraft potential 4 s/c, shifted to SC1 time Power spectrum of spacecraft potential (black) and after treatment by a FIR filter (red). The lower panel shows the phase shift between the original and filtered spectra. s/c potential w/ filter+5-point boxcar filter electric field (GSE) spacecraft potential spacecraft potential 4 s/c on spatial scale The ratio of NIF potential to ion energy loss DE = 1/2 mp (v12 - v22) against Alfven Mach number MA = |vsw· n - vshock|/vA. 2001-03-31 17:14 shock