Electric field, electric potential, and density measurements at quasi-perpendicular collisionless shocks: Cluster/EFW measurements 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 vector electric field (EB = 0) electric field magnitude (EB = 0) spacecraft potential (V) shocks solar wind Spacecraft potential is locally higher (more negative) in the less dense solar wind 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. 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/ FIR filter s/c potential w/ filter+5-point boxcar filter s/c potential w/ filter s/c potential w/ filter :45 shock :14 shock 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) = n 0 + n 1 tanh(k (x-x 0 )) and the 'ramp' is identified as the scale L = |n|/|dn/dx| at x 0. 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 electric field (GSE) electric field magnitude v sw (CIS) electric field (MV) electric field (NIF/MV) NIF electric potential The angle between the timing normal and the maximum variance normal. BN from the timing normal. Shock speed, in the spacecraft frame, as determined by the timing analysis. Shock ramp scale (km) from the hyperbolic tangent fit. Shock ramp scale (c/ pi ) from the hyperbolic tangent fit. SW density is estimated from the spacecraft potential. Apply FIR filter to SCP and electric fields Cross-correlate SCP pairs for time shifts dt ij Calculate timing normal and shock speed from x 12 y 12 z 12 dt 12 x 13 y 13 z 13 n = v dt 13 x 14 y 14 z 14 dt 14 Fit for shock ramp scale (hyperbolic tangent) Boost E to shock frame by (v sh x B) Calculate Maximum Variance normal Rotate to Maximum Variance system Calculate Normal Incidence Frame (NIF) velocity v NIF = n x (v sw x n) and boost E by (v NIF x B) to NIF frame Integrate normal electric field in NIF frame for NIF potential The Recipe NIF electric potential electric field (NIF/MV) electric field (MV) v sw (CIS) electric field magnitude electric field (GSE) spacecraft potential XCF spacecraft potential 4 s/c spacecraft potential 4 s/c, shifted to SC1 time spacecraft potential 4 s/c on spatial scale spacecraft potential 4 s/c spacecraft potential 4 s/c, shifted to SC1 time spacecraft potential 4 s/c on spatial scale E T const 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. The ratio of NIF potential to ion energy loss E = 1/2 m p (v v 2 2 ) against Alfven Mach number M A = |v sw n - v shock |/v A. some conclusions shocks speeds: 10 km/s shock normals: like model? shock ramp scale: c/ pi NIF potentials: V dHT frame is difficult