Langmuir Waves and Electron Acceleration at Heliospheric Shocks by Marc Peter Pulupa A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Stuart Bale, Chair Professor Robert Lin Professor Geoff Bower Spring 2010 Langmuir Waves and Electron Acceleration at Heliospheric Shocks Copyright 2010 by Marc Peter Pulupa Abstract Langmuir Waves and Electron Acceleration at Heliospheric Shocks by Marc Peter Pulupa Doctor of Philosophy in Physics University of California, Berkeley Professor Stuart Bale, Chair Radio waves at the local plasma frequency and its harmonic are generated upstream of collisionless shocks in foreshock regions which are magnetically connected to the shock. The radio waves are created in a multi-step process which involves the acceleration of electrons at the shock front, growth of electrostatic Langmuir waves driven by the accel- erated electron beam, and conversion of the Langmuir waves into radio waves. These radio waves can be used to remotely determine properties of the shock. For example, Type II solar radio burst observations yield information about the radial speed and angular extent of the coronal mass ejection-driven shock associated with the burst. However, in order to completely understand the generation of the radio waves and inter- pret the remote observations, in situ spacecraft measurements of the shock-accelerated electrons and Langmuir waves are necessary. In this thesis, a brief introduction to the heliospheric environment is followed by a survey of the basic principles of collisionless shocks, a detailed discussion of the process of generating shock-accelerated electrons and the resulting plasma waves, and a description of the relevant instrumentation on board the Wind and STEREO spacecraft. Following this review material, several results based on in situ observations are presented: (1) High cadence electron measurements made by Wind in the foreshock region of several IP shocks allow for a determination of the spatial scales of the source regions of Type II radio bursts. The sizes of the observed foreshock source regions are comparable to the size of the terrestrial bow shock. (2) Langmuir waves upstream of IP shocks can be used as a diagnostic signature of foreshock electrons. Using a large database of shocks observed by Wind, different shock parameters are statistically tested for their effectiveness at accelerating electrons. (3) Using a new type of electron detector on STEREO, the limits of the Fast Fermi theory for electron acceleration at suprathermal energies are examined. Preliminary results suggest that the mechanism may hold beyond the regime where the Larmor radius of electrons is much smaller than the scale sizes of the shock. The prospects for future work in this area are discussed in the conclusion, and a description of an experimental antenna calibration procedure known as rheometry is included as an appendix. 1 for Vincente and Feliciana Pulupa i Contents List of Figuresv List of Tables vii 1 Introduction1 1.1 The Sun....................................1 1.2 The Heliosphere and the Solar Wind....................2 1.3 The Solar Wind as a Plasma Physics Laboratory..............3 1.4 Solar Impacts on the Earth and Humanity.................4 1.5 Goals of this Thesis..............................5 2 Collisionless Shocks7 2.1 General Properties of Shocks.........................7 2.2 Collisionless Shocks..............................8 2.3 Collisionless Shocks in the Heliosphere...................9 2.4 MHD Wave Modes.............................. 12 2.5 Shock Parameters and the Rankine-Hugoniot Relations.......... 15 2.6 Observations.................................. 19 2.7 Length Scales in Collisionless Plasmas................... 21 2.8 Particle Acceleration............................. 24 3 Electron Acceleration, Plasma Waves, and Radio Emission 29 3.1 Radio Observations.............................. 29 3.2 Solar Wind Electrons............................. 30 3.3 Electron Acceleration: The Fast Fermi Model............... 33 3.4 Electron Beams and Landau Resonance................... 37 3.5 Langmuir Wave Structure and Mode Conversion.............. 42 3.6 Radio Bursts, CMEs, and Shock Tracking................. 45 3.7 Thermal Noise................................. 45 ii 4 Instrumentation 51 4.1 Wind and STEREO............................. 51 4.2 Electric Field/Plasma Waves......................... 54 4.3 Magnetic Field................................ 56 4.4 Electrostatic Detectors............................ 57 4.5 Suprathermal Electrons............................ 58 5 Interplanetary Foreshock Regions 61 5.1 Introduction.................................. 61 5.2 Event Selection................................ 63 5.3 Foreshock Electron Observations....................... 65 5.4 Shock-Perpendicular Scale Height...................... 71 5.5 Estimating Shock-Parallel Distance..................... 71 5.6 Upstream IMF and coplanarity of shock front............... 74 5.7 Discussion................................... 75 6 Upstream Langmuir Waves 79 6.1 Introduction.................................. 79 6.2 Brief Review of Fast Fermi Theory..................... 82 6.3 Shock Database and Langmuir Wave Detection Algorithm........ 84 6.4 KS Test and Parameter Testing....................... 87 6.4.1 Test Procedure............................ 87 6.4.2 Tested Parameters.......................... 88 6.5 Results..................................... 90 6.6 Discussion and Summary........................... 95 7 Upstream Electron Beam 97 7.1 STEREO Early Orbit............................. 97 7.2 Reflected Electron Beam........................... 100 7.3 Loss Cone Dynamics............................. 108 7.4 Continuing Work with Foreshock Electron Beams............. 113 8 Summary and Future Work 115 8.1 Summary................................... 115 8.2 Future Work.................................. 116 Bibliography 119 A Antenna Calibration 137 A.1 Introduction: Antennas............................ 137 A.2 Rheometry Theory.............................. 138 A.2.1 Impedance of the Rheometry Model................. 138 iii A.2.2 Boundary Conditions......................... 140 A.3 Construction................................. 142 A.3.1 Tank Construction.......................... 142 A.3.2 Manipulator.............................. 143 A.3.3 Model Construction.......................... 144 A.4 Measurement................................. 144 A.4.1 Mechanical Setup........................... 144 A.4.2 Electronics............................... 146 A.5 Analysis.................................... 150 A.6 Results for S/WAVES............................ 151 A.7 Rheometry as a Complementary Technique................. 151 A.7.1 Rheometry and Computer Simulations............... 151 A.7.2 Rheometry and In-flight calibration................. 154 B Formulae 155 iv List of Figures 2.1 Shocks in the heliosphere........................... 13 2.2 Friedrichs diagram for the different MHD wave modes........... 14 2.3 Shock parameters in the upstream and downstream regions of a shock.. 16 2.4 Difference between fast and slow mode shocks................ 18 2.5 Bow shock crossings observed by the Wind spacecraft........... 20 2.6 Rankine-Hugoniot relations at a typical interplanetary shock........ 22 2.7 Diffusive shock acceleration.......................... 26 2.8 Shock drift acceleration............................ 27 3.1 Signal chain for generation of radio emission at the plasma frequency... 31 3.2 Parallel and perpendicular cuts through a solar wind electron distribution function..................................... 34 3.3 Magnetic mirroring.............................. 35 3.4 Geometry of the NIF and HTF........................ 36 3.5 Fast Fermi acceleration at nearly perpendicular shocks........... 37 3.6 Examples of reduced distribution functions: undisturbed, with an electron beam, and with a relaxed beam........................ 40 3.7 Two foreshock Langmuir wave events..................... 42 3.8 The three-wave concept of mode conversion................. 43 3.9 Linear mode conversion............................ 44 3.10 Two regimes of electron antenna noise.................... 47 3.11 Schematic thermal noise spectrum...................... 48 3.12 QTN spectra measured in the solar wind................... 49 4.1 Wind spacecraft with locations of instruments shown............ 52 4.2 STEREO orbit................................. 53 4.3 STEREO Behind spacecraft with locations of instruments shown..... 53 4.4 Wind/3DP electrostatic detectors....................... 58 4.5 The STEREO SWEA and STE detectors.................. 59 4.6 STE-D look directions............................ 60 v 5.1 Cartoon of shock structure consistent with our observations........ 64 5.2 Radio wave, magnetic field, and GOES x-ray data for three shock crossings seen by the Wind spacecraft.......................... 66 5.3 Electron velocity distributions measured by the EESA-L instrument on Wind during the upstream pre-foreshock, foreshock, and downstream pe- riods for the three IP shocks.......................... 69 5.4 In situ particle and wave data from the Wind spacecraft for the three shock crossings................................. 70 5.5 In situ particle data from the Wind 3DP instrument illustrating the ve- locity dispersed electron beam......................... 73 6.1 Fast Fermi process for reflection