One-Dimensional Spacecraft Formation Flight Testbed for Terrestrial Charged Relative Motion Experiments by Carl R. Seubert B.E., Aeronautical (Space) Engineering with Honours, University of Sydney, Australia, 2004 M.S., Aerospace Engineering, University of Missouri - Rolla, USA 2007 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Aerospace Engineering Sciences 2011 This thesis entitled: One-Dimensional Spacecraft Formation Flight Testbed for Terrestrial Charged Relative Motion Experiments written by Carl R. Seubert has been approved for the Department of Aerospace Engineering Sciences Dr. Hanspeter Schaub Dr. Penina Axelrad Dr. Daniel Moorer Dr. Zoltan Sternovsky Date The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. Seubert, Carl R. (Ph.D., Aerospace Engineering) One-Dimensional Spacecraft Formation Flight Testbed for Terrestrial Charged Relative Motion Experiments Thesis directed by Dr. Hanspeter Schaub Spacecraft operating in a desired formation offers an abundance of attractive mission ca- pabilities. One proposed method of controlling a close formation of spacecraft is with Coulomb (electrostatic) forces. The Coulomb formation flight idea utilizes charge emission to drive the spacecraft to kilovolt-level potentials and generate adjustable, micronewton- to millinewton-level Coulomb forces for relative position control. In order to advance the prospects of the Coulomb formation flight concept, this dissertation presents the design and implementation of a unique one-dimensional testbed. The disturbances of the testbed are identified and reduced below 1 mN. This noise level offers a near-frictionless platform that is used to perform relative motion actuation with electrostatics in a terrestrial atmospheric environment. Potentials up to 30 kV are used to actuate a cart over a translational range of motion of 40 cm. A challenge to both theoretical and hardware implemented electrostatic actuation develop- ments is correctly modeling the forces between finite charged bodies, outside a vacuum. To remedy this, studies of Earth orbit plasmas and Coulomb force theory is used to derive and propose a model of the Coulomb force between finite spheres in close proximity, in a plasma. This plasma force model is then used as a basis for a candidate terrestrial force model. The plasma-like pa- rameters of this terrestrial model are estimated using charged motion data from fixed-potential, single-direction experiments on the testbed. The testbed is advanced to the level of autonomous feedback position control using solely Coulomb force actuation. This allows relative motion repositioning on a flat and level track as iv well as an inclined track that mimics the dynamics of two charged spacecraft that are aligned with the principal orbit axis. This controlled motion is accurately predicted with simulations using the terrestrial force model. This demonstrates similarities between the partial charge shielding of space-based plasmas to the electrostatic screening in the laboratory atmosphere. Dedication To Jill Seubert, because you read this out of love, not learning. vi Acknowledgements This research and dissertation would not have been possible without my advisor Dr. Hanspeter Schaub. Your technical prowess and Swiss efficiency are inspirational to me. You facilitated the development of my work as well as my character as a student and as a person. I thank you for your influence, time, guidance, and continued support throughout all the endeavors of my research. I would also like to thank the members of my committee; Dr. Penina Axelrad, Dr. Webster Cash, Dr. Daniel Moorer, and Dr. Zoltan Sternovsky. Thanks is also deserved of some notable figures in the Aerospace Engineering Sciences De- partment. Firstly, Joe Tanner, the great astronaut who has walked in space and now walks next to me in the hallway. You are an idol and I thank you for your truthful words and fun times. Ann Brookover, the `mother' of the graduate student body, we are in gratitude for your hard work, supporting the students and Department. I also thank the graduate students at CU who make the Department so vibrant, fun and intelligent. I personally thank Seebass, whether on the singletrack or the porch we both got through it together, thanks mate. I thank all my friends, both in boulder and abroad, for riding the roller coaster of life's thrills with me. My parents, Reiner and Julianne Seubert deserve a thanks as large as the ocean physically between us. Your unequivocal support has motivated me to reach for the stars without apprehension, and I am grateful. Finally, I thank my wife, Jill. You are by my side without question and illuminate my life with an unparalleled joy and passion. I am so fortunate to have you during these times and forever more. vii Contents Chapter 1 Introduction 1 1.1 Spacecraft formation flight . .2 1.2 The challenges of formation flight . .6 1.3 Coulomb formation flight . .7 1.4 Motivation of research . 11 1.5 Goals of research . 12 1.6 Related work . 12 1.6.1 Theoretical and numerical studies . 12 1.6.2 Existing formation flight testbeds . 15 1.7 Testbed challenges . 16 1.8 Overview of research . 18 1.8.1 Perform terrestrial electrostatic relative motion experiments . 19 1.8.2 Quantify and mitigate external disturbances . 19 1.8.3 Model terrestrial Coulomb forces and compare atmospheric interactions to shielding from a space plasma . 19 1.8.4 Perform autonomous feedback position control experiments . 20 1.9 Thesis overview . 20 2 Earth orbit plasmas and spacecraft interactions 21 2.1 Earth plasma environment . 21 viii 2.1.1 Plasma Debye lengths . 22 2.1.2 On-orbit plasma measurements . 24 2.1.3 Representative plasma parameters for this research . 30 2.2 Spacecraft plasma interactions . 30 2.2.1 Natural charging on GEO spacecraft missions . 31 2.2.2 Natural charging at LEO altitudes . 31 2.2.3 Spacecraft charging concerns . 32 2.2.4 Artificial spacecraft charging . 33 2.3 Spacecraft plasma currents . 33 2.3.1 Charging currents . 34 2.3.2 Primary electron and ion current density . 35 2.3.3 Photoelectron current . 36 2.3.4 Secondary electrons and backscattered emission currents . 38 2.3.5 Net plasma current density . 41 2.4 Double Maxwellian plasma representations and current density . 42 2.5 Numerically computing plasma currents . 43 2.5.1 Dominant charging currents . 44 2.5.2 Net plasma current . 46 2.5.3 Plasma equilibrium currents and floating potentials . 47 2.6 Active charge control in space . 49 2.6.1 LEO charging missions . 50 2.6.2 GEO charging missions . 51 2.6.3 Charge control hardware . 52 2.7 Summary . 53 3 Coulomb force modeling 56 3.1 Coulomb force modeling in a vacuum . 56 ix 3.1.1 Force between point charges . 56 3.1.2 Force between sphere and point charge . 57 3.1.3 Force between finite spheres . 58 3.2 Vacuum model verification with numerical analysis . 64 3.3 Simplified analytic Coulomb force modeling in a plasma . 66 3.3.1 Electrostatic field about a charge . 67 3.3.2 Force between sphere and point charge . 69 3.3.3 Force between finite spheres . 70 3.4 Spacecraft and plasma energies . 72 3.5 Effective Debye lengths and Coulomb forces . 72 3.6 Summary . 73 4 Space-based Coulomb relative motion estimation 75 4.1 Motivation and setup . 76 4.2 Batch estimation development . 76 4.3 Estimating plasma Debye length . 79 4.4 Estimating the potential of one craft . 82 4.5 Summary . 85 5 The Coulomb testbed 87 5.1 Coulomb testbed overview . 87 5.2 Hardware apparatus . 89 5.3 Testbed operations . 93 5.3.1 Safety . 93 5.3.2 Autonomous operations . 95 5.3.3 Experimental maneuver durations . 95 5.4 Apparatus characteristics . 96 5.4.1 Laser position noise . 96 x 5.4.2 Power supply response characterization . 96 5.5 Testbed disturbance identification and mitigation . 99 5.5.1 Mechanical disturbances . 99 5.5.2 Electrostatic disturbances . 103 5.6 Summary . 110 6 Terrestrial Coulomb relative motion experimental results 111 6.1 Candidate terrestrial force model . 111 6.1.1 Attractive force model parameters . 113 6.1.2 Repulsive force model parameters . 114 6.2 Parameter fitting using actuation experiments . 114 6.2.1 Terrestrial and plasma force shielding parameters . 116 6.2.2 Actuation force signal to noise ratios . 118 6.3 Autonomous feedback position control experiments . 119 6.3.1 Constrained 1-D charged relative orbit dynamics . 121 6.3.2 Testbed charge feedback control law . 125 6.3.3 Sloped-track position control experimental results . 126 6.4 Comparing experimental results to simulations with terrestrial model . 129 6.5 Summary . 134 7 Application: tethered Coulomb structures 136 7.1 Tethered Coulomb structure as a GEO sensor platform . 137 7.2 Space tethers . ..