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IEPC-2007-288

Course: PHYSICS 288, Fall 2008
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Hardware Flight Development of Colloid Microthruster Technology for the Space Technology 7 and LISA Missions IEPC-2007-288 Presented at the 30th International Electric Propulsion Conference, Florence, Italy September 17-20, 2007 John K. Ziemer *, Thomas M. Randolph, and Manuel Gamero-Castao Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109 Vlad Hruby , William Connolly, Nathaniel...

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Hardware Flight Development of Colloid Microthruster Technology for the Space Technology 7 and LISA Missions IEPC-2007-288 Presented at the 30th International Electric Propulsion Conference, Florence, Italy September 17-20, 2007 John K. Ziemer *, Thomas M. Randolph, and Manuel Gamero-Castao Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109 Vlad Hruby , William Connolly, Nathaniel Demmons, Eric Ehrbar, Roy Martin, Tom Roy, Douglas Spence, Jurg Zwahlen Busek Co., Natick, MA 01760 The NASA New Millennium Program is planning a flight demonstration of Colloid Micro-Newton Thruster (CMNT) technology on the Space Technology 7 (ST7) mission for future applications to precision formation flying missions such as the Laser Interferometer Space Antenna (LISA) mission. Colloid microthrusters are the actuators for the disturbance reduction system (DRS) on the ESA LISA Pathfinder spacecraft along with FEEP microthrusters as part of the ESA LISA Technology Package (LTP). The goal of the ST7 mission is to demonstrate the technologies necessary to meet the nanometer-level precision positioning control requirements of the LISA mission. To achieve this goal, two CMNT clusters with four thrusters each are required to provide thrust resolution <0.1 N and thrust noise <0.1 N/!Hz for thrust levels between 5 and 30 N. Developed by Busek Co. Inc., with support from JPL in testing and design, the CMNT has been developed over the last five years into a flight-ready microthruster system. The development, validation testing, and flight unit production of the CMNTs are described. Development and validation testing has included a single-thruster system level 3400-hour test, propellant and materials compatibility testing, flight cluster-level vibration and thermal vacuum testing, and performance verification tests. Flight unit production of two clusters was completed in February of 2007 with environmental qualification tests immediately following. Currently both units are being reassembled to replace materials found to be incompatible with the propellant at high temperature before qualification tests are repeated. Final delivery of the units is planned for early 2008 with a planned launch and flight demonstration in 2010. R I Introduction ecent interest in high resolution space interferometers, such as the Laser Interferometer Space Antenna (LISA), that require precise position control has created an interest for developing precise, low-thrust propulsion technology. The primary objective of LISA is to detect and measure as yet unobserved gravitational waves produced by compact binary systems and mergers of super massive black holes. However, even interplanetary space is subject to minute disturbances, such as solar wind, radiation, and photon pressure that could mask the influence of gravitational waves on free-floating proof masses. To shield the gravitational wave instrument, LISA consists of a precisely controlled set of spacecraft that follows the array proof masses within approximately 10 nm and provide a disturbance free environment. Calculations have shown that to reach the sensitivity level of interest, the disturbances to the proof masses can be no more than 3!10-15 m s-2 Hz-1/2 in the 3x10-5 to 1 Hz bandwidth 1. * Senior Engineer, Electric Propulsion Group, Jet Propulsion Laboratory, 4800 Oak Grove Drive, M/S 125-109, Pasadena, CA, 91109; John.K.Ziemer@jpl.nasa.gov Currently an Assistant Professor at the University of California, Irvine, CA 92697; mgameroc@uci.edu President, Busek Company, 11 Tech Circle, Natick, MA 01760; vhruby@busek.com 1 The 30th International Electric Propulsion Conference, Florence, Italy September 17-20, 2007 The Disturbance Reduction System (DRS) for each spacecraft consists of position sensors in the Gravitational Reference Sensor (GRS), microthrusters as the actuators, and drag-free control laws that maintain the spacecraft position and cancel out the environmental disturbances, mainly due to solar photon pressure. To measure gravitational waves effectively, the LISA instrument must operate in a drag-free environment with stringent, highresolution requirements on both the pointing and the translation of the spacecraft2,3. The European Space Agency (ESA) and NASA are sponsoring an international Figure 1. ST7 Disturbance reduction system (DRS) concept. cooperative mission to develop and demonstrate the technology that will make these measurements possible. Each agency is developing a technology demonstration payload: NASAs Space Technology 7 (ST7), supported through the NASA New Millennium Program and managed by the Jet Propulsion Laboratory (JPL)4, and the LISA Test Package (LTP) as part of the ESA LISA Program5. Both technology demonstration payloads will be placed on the same spacecraft (previously known as SMART-2) as part of the LISA Pathfinder Mission, scheduled to launch in late 2009 to early 2010. Once launched, the LISA pathfinder spacecraft will be maneuvered to a halo orbit about the Earth-Sun L1 Lagrange point for a six-month mission where all the new technologies will be demonstrated. The technology goals of the ST7 mission are to demonstrate spacecraft position control to 10 nm/!Hz and spacecraft propulsion system thrust noise less than 0.1 N/!Hz over a frequency range from 1 mHz to 5 Hz. These goals are accomplished by measuring the position of two test masses in the GRS (Figure 1)6, which is part of the LTP, and providing the necessary actuation on the spacecraft through drag-free control laws. When ST7 is active, colloid microthrusters will be fired to provide fine spacecraft attitude control. At other times, three clusters of FEEP microthrusters developed by ESA will maintain the spacecraft attitude and provide drag-free operation. This paper describes the NASA ST7 technology development effort in detail, focusing on the flight hardware development of the Busek Colloid Micro-Newton Thruster (CMNT). The initial flight hardware build of both clusters was completed in February of 2007. After passing functional tests as well as vibration and shock environmental testing, both clusters experienced material/propellant incompatibility issues at high temperature (50C) during thermalvacuum testing. Candidate replacement materials have undergone extensive compatibility testing, and currently the clusters are being rebuilt with the new materials before environmental qualification testing is repeated. II Microthruster Requirements ST7 mission requirements were derived to demonstrate the technology capability that meets LISA and other precision formation-flying mission needs (see Table 1 and Refs 1-4). To meet these requirements, ST7 must use the GRS that is part of the ESA LTP as its drag-free sensor. Note that the LTP sensing requirement is not a level 1 requirement on ST7, but is necessary for ST7 to meet its full or minimum mission success criteria. For all the level 1 requirements, the position control and thrust noise requirements must be met over the measurement bandwidth, 1 mHz to 5 Hz. For the operational lifetime, an assessment of the operability of the thrusters must be made including delivered thrust, thrust noise, specific impulse, latencies, controllability, throttleability, and accuracy. The design life for ST7 is 90 days, including a commissioning phase at the beginning of the mission. Lower level propulsion performance requirements are derived from the level 1 requirements and analysis associated with requirements flow down1-4, as shown in Table 2. The thrust range requirement is determined by the need to counter the solar radiation pressure on the spacecraft and provide full control authority in all axes. The thrust noise and resolution requirement are specified to meet the spacecraft position control requirement, with the upper frequency range extended to 5 Hz to accommodate the control loop. Thruster operational lifetime includes the 90day mission design for consumables including propellant, but the thruster lifetime demonstration goal is set at 3,240 hours to accommodate a standard 50% thruster lifetime margin. The biggest difference between the LISA and ST7 requirements is obviously operational life; thus this is the most important area of technology work remaining for the LISA project after the ST7 mission with a lifetime demonstration goal of 65,700 hours (5 years plus 50% margin). 2 The 30th International Electric Propulsion Conference, Florence, Italy September 17-20, 2007 Table 1. ST7 level 1 requirements including full and minimum success criteria. See References 1-4. Technology Requirement Full Success Criteria Minimum Success Criteria LTP Sensing Noise < 5 nm/!Hz < 50 nm/!Hz Spacecraft Position Control < 10 nm/!Hz < 100 nm/!Hz Thrust Noise < 0.1 N/!Hz < 0.5 N/!Hz Control Life > 60 days > 10 days Table 2. Derived ST7 and LISA microthruster propulsion requirements. See References 1-4. Requirement ST7 LISA Thrust Range 5 to 30 N 5 to 30 N* Thrust Precision < 0.1 N < 0.1 N Thrust Noise < 0.1 N/!Hz (5 Hz control loop) < 0.1 N/!Hz (5 Hz control loop) Measurement Bandwidth 1x10-3 to 5 Hz 3x10-5 to 1 Hz Thrust Command Rate 10 Hz (< 0.1 s latency) TBD Thrust Range Response Time < 100 s TBD Specific Impulse > 150 s TBD Operational Lifetime > 2,160 hours (90 days) > 43,800 hours (5 years) Plume Half Angle < 35 (95% beam current) TBD * The LISA thrust range requirement may be lower for the science phase and higher for tip-off recovery The LISA mission has an operational goal of 10 years that will require an additional 3.5 years worth of consumables Environmental temperature requirements for the ST7 CMNT are shown in Table 33. Operational temperature requirements are driven by the viscosity of the propellant at the minimum temperature and the conductivity of the fluid at the maximum temperature to produce the required thrust range. Below the minimum temperature, the fluid viscosity increases to the point where the bellows pressure is not large enough to compensate and provide adequate flow to the thruster head and reach maximum thrust. Fortunately, the ion to droplet ratio of the electrospray decreases with temperature, increasing the thrust for the same current level to provide adequate margin. Conversely, at the highest operating temperatures, the maximum possible propellant flow rate increases with decreasing viscosity, while the thrust decreases for the same current level. The minimum non-operating temperature limit is driven by the risk of freezing the propellant. The maximum non-operating temperature limit has been reduced to 60C due to propellant thermal expansion considerations. Dynamic environmental requirements are shown in Table 43. Table 4. ST7 CMNT dynamic environmental requirements. See Reference 3. Test Axis Frequency (Hz) Flight Levels Protoflight Levels Quasi-Static In Plane N/A 16.0 g 20 g Quasi-Static Out of Plane N/A 20.8 g 26 g Sine Vibe All Axes 5 to 21 8.8 mm 0-pk 11 mm 0-pk 21 to 100 16 g 20 g Random Vibe In Plane 20 0.024 g2/Hz 0.038 g2/Hz 20 80 + 3 dB/octave + 3 dB/octave 80 400 0.096 g2/Hz 0.15 g2/Hz 400 2000 - 5 dB/octave - 5 dB/octave 2000 0.007 g2/Hz 0.010 g2/Hz Overall 8.48 grms 10.6 grms Random Vibe Out of Plane 20 0.048 g2/Hz 0.073 g2/Hz 20 80 + 3 dB/octave + 3 dB/octave 80 400 0.19 g2/Hz 0.29 g2/Hz 400 2000 - 10 dB/octave - 10 dB/octave 2000 0.0009 g2/Hz 0.0014 g2/Hz Overall 9.9 grms 12.3 grms Shock All Axes 100 N/A 20 g 1500 1000 g 10,000 1000 g 3 The 30th International Electric Propulsion Conference, Florence, Italy September 17-20, 2007 Table 3. Environmental requirements at CMNT cluster mounting flange3. Mode Min (C) Max (C) Operating Design 10 30 Protoflight -5 50 Non-Operating Design 0 40 Protoflight -15 60 III CMNT Technology Development The two Colloid Micro-Newton Thruster (CMNT) clusters being developed at Busek Co., Inc.2,3,7,8 each include four complete and independent thruster subsystems: 4 thruster heads, 4 propellant storage and feed control (microvalve) systems, 1 cathode neutralizer, 4 PPUs and 1 DCIU. Thrust is adjustable from 5-30 N by changing the beam voltage (2-10 kV) and/or propellant flow rate that determines the beam current (2.2-5.4 A). Independent, fine control of both the beam current and beam voltage allow for precise control of thrust to better than 0.1 N resolution with <0.1 N/"Hz thrust noise. Figure 2 shows one flight thruster cluster with four thruster subsystems, and Figure 11 (located at the end of the paper) shows a functional block diagram for the CMNT cluster. We will now discuss the subsystems of the Busek CMNT being developed for the ST7-DRS Mission. A. Overview of CMNT Subsystems 1. Thruster Head The thruster head comprises a manifold that feeds nine emitters in parallel, a heater to control temperature and propellant physical properties (i.e. viscosity, conductivity, etc.), and electrodes that extract and accelerate the propellant. The flight design thruster head has been used in single-thruster system test boxes Figure 2. Busek Colloid Micro-Newton Thruster for long-duration testing and performance validation (CMNT) Flight Cluster 1 including four thruster measurements described later in this paper. Some heads, electronics, and cathode neutralizer (visible) in materials used in the manifold have been changed to thermal-vacuum environmental test setup. ensure compatibility with the propellant. 2. Propellant Feed System Propellant is stored in four electrically isolated stainless steel bellows compressed by four constant force springs set to supply four microvalves with propellant at approximately 1 atm of pressure. The microvalve is piezo-actuated using ~1 mW of power to control the propellant flow rate and current to better than 1 nA without significant physical motion. This level of precision corresponds to #0.01 N of thrust, with a response time over its full range of less than 0.5 s. The flight microvalve design has been part of multiple single- and multiple-emitter long-duration tests, accumulating over 15,000 hours of total test time without incident in the design temperature range. Again here materials have been changed to ensure propellant compatibility and microvalve function at high temperature. 3. Cathode Neutralizer The cathode neutralizer developed by Busek is made from a carbon nanotube (CNT) base with an extractor electrode. The cathode is capable of producing 10 A to 1 mA using extraction voltages of 250-800 V. One CNT cathode has been tested alone in an ultra-high vacuum chamber for over 13,000 hours at 100 A without incident. CNT cathodes have also been tested successfully with operating thruster heads during multiple long-duration tests. 4. Thruster Electronics The flight thruster electronics including 4 power processing units (PPUs) and one digital control and interface unit (DCIU) for each cluster have completed qualification testing at the component level. EM and flight electronics have over 8,000 hours of operation under vacuum controlling complete thruster sub-systems. The PPU includes the high-voltage DC-DC converters that have been specifically designed and tested for this application by Busek Co. The DCIU controls all four thrusters and provides the command and telemetry interface to the spacecraft and DRS. The maximum obtainable thrust within the set current and voltage range is expected to be 40 N, and even higher levels (as high as 100 N) can be achieved by directly controlling the microvalve to reach current levels up to 10 A. However, higher current levels lead to more overspray onto the extractor electrode, shortening the available lifetime of the CMNT. The maximum current level of 5.4 A is designed to prevent any overspray while providing >30% margin on the maximum thrust requirement. 4 The 30th International Electric Propulsion Conference, Florence, Italy September 17-20, 2007 IV Microthruster Validation Tests and Flight Production Test validation of the Busek CMNT design for ST7 presents several challenges for a traditional qualification program. The primary challenge is making direct performance measurements with the flight clusters due to the difficulties of sub micronewton resolution thrust stand measurements with such a large mass. Also, since thruster lifetime is expected to be independent of the number of operating thrusters (each thruster head has enough emitters to provide the full thrust range and operates independently in the cluster), assembling and testing an entire cluster to assess lifetime would be expensive, time intensive, and not necessary. To avoid this problem, a validation plan was formulated to perform certain validation tests at the box level, with a single electronics, bellows, microvalve, and thruster combination. Other protoflight tests are performed at the flight cluster level (see Table 5). In this plan, thrust stand measurements necessary for verifying thrust range, precision, noise, response time, and specific impulse requirements are made at the box level, where the small box mass enables reasonably accurate thrust measurements. Using these box level thrust measurements, correlations can be made to validate the determination of thrust from current and voltage measurements. Current and voltage measurements are then made at the cluster level, using the model validated by thrust stand measurements, to estimate thrust at the cluster level. Because lifetime and plume measurements are almost entirely independent of the cluster thermal and structural design, these requirements are also verified at the box level for test simplicity. Because the structural and thermal design of the box is very dissimilar to the cluster design, these requirements are validated at the cluster level by protoflight testing. Table 5. ST7 CMNT simplified validation matrix including status of each test. Requirement Box Level Cluster Level Status Thrust Range Calculations show the flight thrusters meeting Partial ! requirements, preliminary thrust stand data Thrust Precision Partial ! show that the calculations are within 2% of Thrust Noise Partial ! measurements, and final measurements as a Thrust Response Time Partial ! function of temperature are ongoing Specific Impulse Partial ! Operational Lifetime Formal Life Test 2B complete with 3478 hours ! Plume Half-Angle Measurements complete; plume half-angle and ! stability meet or exceed requirements Environmental Dynamics Both flight clusters passed full protoflight-level vibration and shock testing; reassembled ! clusters will be retested at workmanship levels Environmental Temperature Thermal-vacuum testing was performed on both clusters and revealed material/propellant * ! ! compatibility issues that require reassembling the clusters with new materials and retesting *Originally only validated at the cluster level, box level thermal testing will be run in parallel with the flight unit reassembly to test thruster system components. Environmental thermal validation testing will still be conducted at the cluster level as well. A. Formal Life Test 2B The operational time requirement for the ST7 mission is 60 days (1440 hours) total, including the colloid microthrusters. The thrusters have been designed for a 90-day (2160 hour) mission, including consumables and lifetime of all subsystems. To provide for pre-flight ground environmental qualification testing and increase the chance for mission success, 50% margin has been applied to the 90-day lifetime design target, giving a goal for lifetime demonstration of 3240 hours. During the mission, we expect the sun-opposing thrusters to operate at higher thrust levels than the sun-facing thrusters, and these conditions are expected to be more strenuous on the thrusters. With an expected thrust level for the sun-opposing thrusters of 18.0 4.5 N, we expect to require <140 Ns of total impulse, consuming <58 g of propellant over the entire mission. Formal Life Test 2B (FLT 2B) began on May 23rd, 2006 at Busek Co. with a complete, flight-like colloid thruster system, including thruster head, microvalve, propellant feed system, bellows, and electronics3. The test was stopped voluntarily after 172 days on November 10th, 2006. As shown in Figure 3, the CMNT system accumulated 3478 hours of operation, and based on thrust calculations produced 245 Ns of impulse, consuming 113 g of propellant during the entire test (see Figure 4). In addition, many of the performance requirements were tested and validated through calculation during the test (the performance model will be verified by direct thrust measurements). The completion of FLT 2B has validated the lifetime of the thruster head, microvalve, electronics, and bellows (not including all feed system components) for the flight design and in-space operation over the ST7 mission duration. 5 The 30th International Electric Propulsion Conference, Florence, Italy September 17-20, 2007 Figure 3. Graph of calculated thrust over the operational duration of FLT 2B. Daily thrust range and response tests, feed system repair, thrust commands mode, and bellows refill are all indicated. ST7 Mission ST7 Mission Figure 4. Graph of calculated total impulse produced and propellant consumed during FLT 2B. The total impulse production and propellant usage during FLT 2B are both greater than the projected requirements for the sun-opposing thrusters by more than 50%. 6 The 30th International Electric Propulsion Conference, Florence, Italy September 17-20, 2007 1. Detailed chronology of events during FLT 2B The first 500 hours of FLT 2B were focused on removing bubbles from the feed system by running near maximum flow rate (see Ref. 3 for a description of bubble removal). Daily thrust range and response tests allowed the progress of removing bubbles to be observed while operational hours accumulated. Due to bubbles passing out of the emitters, the calculated thrust noise exceeded the 0.1 N/!Hz requirement, but for only the first 232 hours. Bubbles were completely removed from the system by 600 hours of operation, and we expect the flight thrusters to reach bubble-free operation in much shorter periods (10s of hours) due to process improvements. Also, an on-orbit commissioning phase accommodates operation of the thrusters for 100s of hours to pass bubbles before full system operation is required. A slight leak in the propellant feed system near hour 500 of FLT 2B and the subsequent repair (addition of epoxy on exterior of leaking feed system componentno other hardware was removed, touched, or cleaned) provided enough excess propellant to form a ~1 G" path between the beam and extractor electrodes. This level of impedance is not considered a failure (the power processing units are designed to operate effectively with a load as low as 100 M"), and the thruster was set to operate in a low voltage (low thrust) mode until the impedance increased. Fortunately, while the propellant used for the ST7 colloid microthruster has about the same conductivity as seawater, it breaks down slowly into a dielectric at a reasonable voltage and current density. Clearing impedance paths >1 G" caused by excess propellant simply becomes a matter of time at voltage using a controlled process with frequent impedance measurements to indicate progress. Near hour 800, the voltage was once again increased to nominal levels to speed the up clearing process, and the parallel high-impedance path was completely cleared near hour 1000. During the final clearing process, thrust noise once again increased beyond the allowable requirement for approximately 50 hours; however, thrust noise returned to acceptable values for the remainder of the test. Just after 1000 hours, the thruster was set into mission simulation mode with a series of repeating thrust commands provided by the DRS control algorithm team from NASA Goddard. The series of commands, lasting approximately 20 minutes at 10 Hz, allowed the thruster to demonstrate flight-like conditions including fast (100 ms) response to both beam voltage and current (controlled by the microvalve) commands, determined by the onboard software in the thruster DCIU. As shown in the small inset graph of Figure 3, the simulated commands centered around 19 N, and varied by as much as +/- 1 N. The thruster ran successfully in this mode for over 1000 hours of continuous, unattended operation. After 2300 hours of total operation (surpassing the 90-day mission and consumables requirement), the thruster showed signs of running out of propellant, and the average thrust command level was reduced to 6 N to extend the test. At 2366 hours, the thruster finally ran out of propellant, the test facility was opened to refill the bellows, and no other components were touched, removed, or cleaned. The test started again with new software for simulating the ST7 avionics unit, running again with the mission simulation thrust commands repeating successfully for an additional 1000 hours. Using new startup procedures, the thruster operated without any signs of bubbles after only 48 hours beyond the restart after refilling the bellows. The test was stopped voluntarily after 3478 hours of total operation with a successful demonstration of thrust range and performance. The completion of FLT 2B validated the thruster head, microvalve, electronics, and bellows lifetime at the system-level, but leaks in the feed-system required new component designs that were validated in parallel, accelerated lifetests. 2. End of Life Functional Test Results At the end of FLT 2B, after approximately 3472 hours of operation, a functional test was performed to demonstrate the performance of the thruster. As shown in Figure 5, the functional test consisted of demonstrating full thrust range operation in both constant current and constant voltage, low- and high-thrust modes. During each step the response time and accuracy was measured based on thrust calculations from beam voltage and current and found to be within acceptable limits in each case. The time to reach full thrust (30 N within <0.1 N) from the minimum current and voltage levels was found to be approximately 10 s in thrust command mode, with the voltage ramp rate set to 400V/s (adjustable up to 10000 V/s). Response times can be longer if bubbles are present in the feed system; however, by this time in the life test, the thruster was running without any signs of bubbles. Thrust noise was also calculated based on current and voltage measurements during a 1-hour long run at fixed operating conditions. Figure 6 shows graphs of thrust and thrust noise from this period, clearly meeting the ST7 requirement. B. Plume Divergence and Stability Measurements Models and measurements of breadboard and EM-level CMNT exhaust plumes at JPL have shown that no charged particles exit the thruster beyond a 35-degree half-angle at the most divergent operating condition. Mass deposition measurements using a temperature controlled quartz-crystal microbalance have shown that no measurable deposition occurs outside of a 45 degree half-angle. Emissive probe measurements show beam potentials 0-30 V with a constant divergence angle at >10 cm downstream of the thruster head, even without using a neutralizer9. To date, all JPL tests show that the Busek CMNT will meet ST7 and future LISA contamination requirements. 7 The 30th International Electric Propulsion Conference, Florence, Italy September 17-20, 2007 Figure 5. Functional test performed at the end of FLT2B, beginning after 3472 hours of operation. Minimum and maximum thrust was demonstrated as well as slew rates. Figure 6. Calculated thrust and thrust noise from a one-hour run at constant thrust as part of the final functional test of FLT 2B (run began ~100 minutes after the beginning of the functional test). Busek measurements of exhaust beam divergence and stability using a beam target with 56 electrometers (each with ~nA resolution) in a cross pattern are shown in Figure 7. Even for the worst-case conditions of the lowest beam voltage (lowest thrust levels), the exhaust beam half-angle encompassing 95% of the current is <25 deg. (requirement is <35 deg.). Measurements of the exhaust beam centerline location on the beam target over time are shown in Figure 8. While it seems an offset of ~21 mrad (1.2 deg.) is present from misalignment of the beam target with the thruster exhaust, the location of the beam centerline is stable and meets requirements (<2.5 mrad/"Hz) over the measurement bandwidth of 1 mHz to 5 Hz. Higher noise levels at lower frequency are due to electrometer drift in the beam collector sensors. These direct measurements of exhaust beam divergence and stability confirm the previous plume measurements taken at Busek and JPL. 8 The 30th International Electric Propulsion Conference, Florence, Italy September 17-20, 2007 Figure 7. 56-channel electrometer/plume collector used for divergence measurements and graph of plume half-angle (includes 95% of current) for various beam voltage and thrust levels showing all conditions are below the 35 deg. requirement. Figure 8. Measurement of the thrust vector angle relative to a perpendicular centerline from the thruster exit plane over time and PSD plot showing thrust vector noise is below the requirement. C. Dynamics Environmental Validation To meet the dynamic environmental requirements specified in Table 4, a combination of testing on the flight units and a structural mock up was performed. Shock testing was performed on a structural mock up of the flight cluster due to concerns about damaging the flight clusters with protoflight level loads. The structural mock up was nearly identical to the flight cluster. The only significant differences were mass mock-ups used for three of the four PPUs, microvalves and thruster heads, and the DCIU. This configuration was justified because all the flight components, except the DCIU, were tested to the protoflight shock levels at flight positions. Due to the structural isolation for the DCIU located on the -x axis of the cluster, it was not considered necessary to shock the DCIU because the resulting dynamic loads would be enveloped by flight cluster vibration testing. Shock testing was performed by impact hammer at the Dayton T. Brown, Inc. facility with the cluster mounted on the x-axis for all testing. Cluster component verification of shock environment survival included pre- and post-visual inspections of the bellows and cathode assemblies, alignment measurements of the thruster head emitters, flow and leak testing of the microvalve, and electrical testing of the PPU. No significant differences were observed between the pre- and post-test performance and inspection measurements; thus, the cluster shock requirement has been validated. Sine, random, and quasi-static load testing was performed on both clusters with a vibe table at NTS, Inc. The clusters and mass dummy were all mounted on a vibe fixture to interface with the vibe table (Figure 10). Eight three-axis force transducers were placed between the cluster flange and the vibe fixture. These force transducers were used for force limiting according to the quasi-static limits defined in Table 4. Two three-axis control accelerometers were placed on the vibe fixture top flange, for control to the required spacecraft dynamic interface levels. Three three-axis response accelerometers were placed on the cluster to measure the resulting response 9 The 30th International Electric Propulsion Conference, Florence, Italy September 17-20, 2007 Figure 10. Picture of CMNT flight cluster 1 mounted on vibe table (left) and a CAD drawing showing the location of force transducers (blue) and response accelerometers (red). (Figure 10). Loads were initially set using a mass dummy in each axis. Cluster 1 was tested to the flight acceptance levels defined in Table 4 while cluster 2 was tested to protoflight levels. Pre- and post-testing of both clusters included functional testing of the clusters and visual inspections. No significant differences were observed between the pre- and post-test functional and inspection measurements; thus, the cluster vibe requirement has been validated. When the flight clusters are reassembled, both clusters will be submitted to workmanship-level vibe testing. D. Thermal Environmental Validation After successfully passing dynamic environmental testing, both clusters entered into thermal vacuum (TVAC) environmental testing. The expected environment on the spacecraft for the colloid thruster clusters is in the shade of the solar panels with heaters at the cluster flange and in the thruster heads running to maintain operating temperature. As shown in Table 3, the normal operating range of the colloid thruster is from 10C to 30C with the non-operating temperatures below and above the operating temperature by 10C. Protoflight levels are set 15C below the minimum temperatures and 20C above the maximum temperature to demonstrate adequate margin. For TVAC testing, as shown in Figure 9, a flange temperature profile including thermal cycling and soaking was developed to qualify clusters one at a time. A 3 m diameter, high-vacuum facility with a liquid nitrogen cooled shroud to simulate the Figure 9. Temperature profile for thermal vacuum radiative background of space was used for the qualification testing of the CMNT clusters. thermal qualification testing. 10 The 30th International Electric Propulsion Conference, Florence, Italy September 17-20, 2007 Thermal balance testing of the flight units will not be performed until spacecraft integration; however, a thermal balance test of a cluster mock-up was performed in the test facility to provide preliminary validation of the cluster thermal model. The purpose of these thermal environmental tests was to qualify the thrusters for the expected thermal environment as, up to that point, only component level testing had occurred at temperatures outside of the design range (including the lifetest that had operated for more than 3400 hours between 10-30C). At the component level, the electronics had already been put through full environmental testing, and a flight-like thruster head manifold had already been put through thermal cycle and soak tests. During the 50C soak stage near the end of the first full flight-cluster TVAC test (and after passing through each previous stage successfully), cluster 1 experienced feed system issues that had not been observed in any previous testing of the flight or developmental hardware. From evidence uncovered during thruster disassembly, a failure investigation team (including members from both Busek and JPL) found that a seal material used in the feed system was not compatible with the propellant at high temperatures, and was found to be the most probable cause of the feed system issues. The failure investigation teams main recommendation was that the material be replaced throughout each thruster feed system, as well as other minor recommendations that will not be described here. E. Material Compatibility Testing and Flight Cluster Reassembly While other design alternatives were considered, the most expedient solution to the issues found during thermal vacuum testing was to replace the affected materials with an alternative that was compatible with the propellant (no shape or functional change was made to any of the replacement hardware). Extensive testing including measurements of material properties before and after long duration (up to 1100 hours) exposure to propellant at high temperature led to two candidate materials that both appeared to be compatible with the propellant by material property evaluations. Outgassing measurements revealed one to be more favorable, and measurements taken after a long duration propellant exposure at elevated temperatures showed that the residual propellant contained <0.1% of the new material, making it the final selection. Once the material selection was complete and the other minor recommendations from the failure investigation team were implemented as well, component level testing of the feed system began with propellant exposure tests at 60C. To date, all components have passed initial tests, and reassembly work of the two flight clusters has commenced. After reassembly is complete, the clusters will again be put through functional, dynamic and protoflight level thermal environmental qualification testing. V LISA Colloid Microthruster Technology Development Two major concerns exist for demonstrating the extended colloid microthruster lifetime requirement for LISA: clogging of emitters and overspray onto the electrodes. Bubbles in the feed system also present a performance issue and can impact lifetime by periodically increasing overspray when a bubble reaches an emitter tip. While all of these problems have been addressed to satisfy ST7 lifetime requirements (demonstrated during FLT 2B), extending the lifetime to LISA requirements will necessitate additional component development with as much flight heritage taken from ST7 experience as possible. Specifically, a new emitter design that prohibits bubbles from forming in the feed system and significantly improves emission stability, reducing overspray and improving performance, has already been demonstrated in operation. In initial testing of this emitter design, over 1000 hours of operation were accumulated withou...

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INDUCTION: INFERENCE AND PROCESS Neal J. Rothleder The University of Michigan 3218 EECS Building, 1301 Beal Ave., Ann Arbor, MI 48109-2122 nealr@umich.eduAbstract Despite the variety of discussions on induction, there is still no explicit definitio
Michigan - PHYSICS - 290
Helicon Double Layer ThrustersIEPC-2005-290Presented at the 29th International Electric Propulsion Conference, Princeton University, October 31 November 4, 2005 C. Charles, P. Alexander, C. Costa, O. Sutherland, R.W. Boswell Plasma Research Labora
Michigan - PHYSICS - 334
AEDC plume measurements using bi-directional ion flux probesIEPC-2007- 334Presented at the 30th International Electric Propulsion Conference, Florence, Italy September 17-20, 2007 Yevgeny Raitses * Princeton Plasma Physics Laboratory, Princeton, NJ
Michigan - PHYSICS - 340
Midterm #4 Practice Exam Questions - SolutionsTopics in relativity: Michelson-Morley and ether drift Postulates of special relativity Simultaneity Lorentz transformations Length contraction Relativistic velocity addition Relativistic Doppler effect
Michigan - PHYSICS - 340
Ground-Based Experiment of Current Collection to Bare Tether in High-Speed Magnetized PlasmaIEPC-2007-340Presented at the 30th International Electric Propulsion Conference, Florence, Italy September 17-20, 2007 Hirokazu Tahara* Osaka Institute of T
Michigan - PHYSICS - 390
Search for Exotic Baryons Standard Quark Model classifies hadrons as mesons ( qq ) baryons ( qqq ) -&gt; surrounded by pion cloud or qq vacuum polarizationor The Search for Exotic BaryonsPhysics 390 Fall 20065 April 2006 also allows non-stand
Michigan - PHYSICS - 401
c J. Fessler, January 2, 2001, 17:251Examples of EECS 401 Prerequisite Material (Not Necessarily Completely Inclusive)Differentiation from First Principles f (x + ) f (x) f (x) f (x ) d f (x) = lim+ = lim+ , dx 0 0 where 0+ means approac
Michigan - PHYSICS - 401
Review of basic probability and statisticsProbability: basic denitions A random variable is the outcome of a natural process that can not be predicted with certainty. Examples: the maximum temperature next Tuesday in Chicago, the price of Wal-Mar
Michigan - PHYSICS - 401
Review of basic probability and statisticsProbability: basic denitions A random variable is the outcome of a natural process that can not be predicted with certainty. Examples: the maximum temperature next Tuesday in Chicago, the price of WalMart
Michigan - PHYSICS - 420
Geophysics 420 Outline 11 Amplitude of seismic waves The amplitude of seismic waves changes due to a variety of factors. The energy in seismic waves decays due to geometric spreading (as 1/r 2 for body waves and 1/r for surface waves) and changes due
Michigan - PHYSICS - 420
Problem set 1. Due Friday 9/16/051. Measure the absolute value of the acceleration of gravity. Treat this as a standard physics experiment by providing a complete description of goal, experimental setup, measurements, interpretation (including erro
Michigan - PHYSICS - 420
GS420 Geophysics - Outline 3Moment of inertia The denition of the moment of inertia is I= r 2 dm = V r 2 dV M2 3(1)where r is the distance of the innitesimal element dm or dV to the rotation axis. For the long thin rod used previously we nd t
Michigan - PHYSICS - 420
Problem set 4. Due October 14 1. Assume that a mountain of 4 km high exists in isostatic equilibrium with normal continental crust of 30 km thick. The crustal density is 2.8 and that the mantle density is 3.3. a) Calculate the thickness of the crusta
Michigan - PHYSICS - 438
33rd Telecommunications Policy Research Conference, Sept. 2005How Americas Fragmented Approach to Public Safety Wastes Money and Spectrum Jon M. Peha1Carnegie Mellon UniversityAbstractEmergency responders such as firefighters, police, and parame
Michigan - PHYSICS - 441
Internet Governance: Theory and First Principles Johannes M. Bauer* Michigan State University Preliminary draft, August 31, 2005 For purposes of discussion only1. Introduction For many years, the Internet was regarded as a space that should not and
Michigan - PHYSICS - 442
End of Life Care, Euthanasia, and the IncompetentReaction Statements 3 and 4 Number3 was graded out of 10 points instead of 12 4 will be 12 points Assignment Crucialto practiceOne clear sentence (bold or underline) stating each actual arg
Michigan - PHYSICS - 442
What is the nature of mind, perception and reality? (of key importance to psychology) Course explores the connections between perception to science and reality Non-conventional approach to studying the psychology of mind and the nature of human perce
Michigan - PHYSICS - 442
CSM MiniDAQ Quickstart GuideUniversity of MichiganAugust 29, 2001 J. GregoryContentsSection 1. Introduction to the CSM MiniDAQ 2. Starting the CSM DAQ . . 3. JTAG Programming . . 3.1 Connecting the hardware . 3.2 Enabling the JTAG serial connec
Michigan - PHYSICS - 450
0.0614429935813 0.0278114564717 -0.00472683506086 -0.0110163791105 -0.00491652451456 -0.00366433849558 -0.00147688400466 0.00468915700912 0.000263888388872 -0.00637193256989 -0.00784652028233 -0.00961081311107 0.00104263715912 -0.00379575230181 -0.00
Michigan - PHYSICS - 450
3.12162214651e-22 2.92811286484e-22 2.83734491142e-22 2.85489015733e-22 2.8572262546e-22 2.81786496561e-22 2.83088386118e-22 2.86405450873e-22 2.87389017004e-22 2.82458941928e-22 2.80534231732e-22 2.80920150607e-22 2.81815308086e-22 2.812303527e-22 2
Michigan - PHYSICS - 460
Data Flow Simulations through the ATLAS Muon Front-End ElectronicsJ. Wehrley Chapman, University of Michigan (email: umjwc@umich.edu) AbstractA VerilogHDL simulation of the data flow along the readout chain of the ATLAS MDT front-end is presented.
Michigan - PHYSICS - 463
EXPLORATORY RESEARCH ON THE USE OF ACTIVITY CAPTURE TECHNOLOGY IN THE ARCHIVING AND DISSEMINATION OF DISCIPLINE SPECIFIC LECTURES AND ADVANCED TRAINING MATERIALSIntroductionWe request herein a sum of xxx to fund a specific set of exploratory studi
Michigan - PHYSICS - 489
ATLASCSM-0/MiniDaq Hardware Notebook Firewire Setup CSM cardPC/VME Setup MultiplexerJanuary 26, 2000 - J. Wehrley Chapman
Michigan - PHYSICS - 497
AM - MC Public Sector SpectrumDraft September 8, 2005.Getting the best out of public sector spectrum Adele Morris, U.S. Department of the Treasury1 Martin Cave, Warwick Business School, UK Abstract The paper addresses the general problem associat
Michigan - PHYSICS - 497
M I C H I G A N AT L A S M O N I T O R E D D R I FT CHAMBER PRODUCTION DATA B A S EFebruary 4, 2000Homer A. Neal, Shawn McKee and Chunhui Han Department of Physics University of Michigan Ann Arbor, Michigan 48109The University of Michigan ATL AS
Michigan - PHYSICS - 499
'aTRANSFORMATIONScomparative study of social transfomtionsCSST WORKING PAPERSThe University of Michigan Ann Arbor&quot;Reclaiming the Epistemological 'Other': Narrative and the Social Constitution of Identity&quot; Margaret R. Somers and Gloria D. Gi
Michigan - PHYSICS - 499
M I C H I G A N AT L A S MONITORED DRIFT C H A M B E R P RO D U C T I O N DATA BA S EFEBRUARY 4, 2000HOMER A. NEAL, SHAWN MCKEE AND CHUNHUI HAN DEPARTMENT OF PHYSICS UNIVERSITY OF MICHIGAN ANN ARBOR, MICHIGAN 48109THE UNIVERSITY OF MICHIGAN ATLA
Michigan - PHYSICS - 508
February 8, 2002 METAMORPHIC PETROLOGY 508 Lecture 12. Metamafic Rocks II next lecture Monday: continue metagranitic rocks: Chap. 9, Spear, esp. p. 304-327 experimental studies of greenschist-amphibolite-granulite transitions for real rock compositio
Michigan - PHYSICS - 508
April 15, 2002 GS508. METAMORPHIC PETROLOGY Lecture 30: &quot;Ultra-Ultra&quot; High Pressure Metamorphism (UUHPM) Wednesday lecture: fluid flow during metamorphism readings: Spear, Chap. 19, 673-710 UUHPM arbitrarily defined as rocks that attained stishovite
Michigan - PHYSICS - 516
Reference books for medical imaging The first 3 of these should be on reserve at Engineering Library for EECS 516 @b prince:05 Prentice-Hall . 2005 Jerry L Prince Jonathan M Links Medical imaging signals and systems @an ISBN: 0130653535 @b macovski:8
Michigan - PHYSICS - 516
Lecture-by-lecture list of topics EECS 516 Medical Imaging Systems, F07 'X' means a topic covered in a previous year's lecture but not this year! (such topics are usually still in the lecture notes and are recommended reading) 1 (1) Introduction Over
Michigan - PHYSICS - 516
EECS 516 Fall 2007Medical Imaging Systems 2233 GGBL, Tue Thur 3:30-5:00 PMInstructor: Professor Jeff Fessler Email: fessler AT umich DOT edu Office: 3401 EECS Phone: 763-1434 Office Hours: TBA (see web site or office door) Web: http:/www.eecs.umi
Michigan - PHYSICS - 516
EECS 516 Syllabus (Tentative!) Subject Source Material (PL=Prince &amp; Links) (+ lecture notes for most topics) PL 1 1 2 LecturesIntroductionReview PL 2, JF 1 Linear Systems Probability / Random Processes (?) Ultrasound PL 10,11 6 Basic 2-D Image Pr
Michigan - PHYSICS - 520
Problem Set 4 Physics 520Fall 2005 L. Sander 10/13/05 due 10/20/051. Consider a linear chain of atoms of alternating mass interacting via the Lennard-Jones nearest neighbor potential. a.) Solve for the dispersion relation and exhibit the optical m
Michigan - PHYSICS - 520
Problem Set 2 Physics 520Fall 2005 L. Sander 9/22/05 due 9/29/051. a.) Explicitly construct the reciprocal lattices for simple cubic, body-centered cubic, and fcc lattices. b.) Show that the reciprocal lattice of the reciprocal lattice is the dire
Michigan - PHYSICS - 521
Course AnnouncementPhotonic CrystalsEECS 598, Section 002, Fall 2007 Instructor. Almantas Galvanauskas, almantas@eecs.umich.edu, phone: 615-7166, room ERB I 6102 Meeting schedule. M W 1:30pm 3:00pm, 1121 LBME Course Content As a result of recent
Michigan - PHYSICS - 611
4.1Theorems of Alternatives for Systems of Linear ConstraintsKatta G. Murty, IOE 611 Lecture slides System of constraints is Feasible if it has a feasible solution, i.e., one satisfying all constraints in it. Infeasible if it has no feasible solut
Michigan - PHYSICS - 611
Course Description, 611, Sp/Sum 021University of Michigan School of Social WorkCOURSE TITLE: Theories of Social Change (including Societal, Community and Organizational levels and how individual change is related to change at larger system level
Michigan - PHYSICS - 625
0.0566581301391 0.00281607173383 -0.0295413117856 -0.0350922979414 -0.0505063198507 -0.0333682894707 -0.0284948050976 -0.0294864345342 -0.0260722339153 -0.0204453077167 -0.032401651144 -0.0390029661357 -0.0355508439243 -0.0288251433522 -0.02911676838
Michigan - PHYSICS - 646
Combustion Theory and Modelling Vol. 9, No. 4, November 2005, 617646Characteristic boundary conditions for direct simulations of turbulent counterow ames C. S. YOO, Y. WANG, A. TROUVE and H. G. IM Department of Mechanical Engineering, University
Michigan - PHYSICS - 650
4.48159389958e-22 4.34525959146e-22 4.29428204547e-22 4.35879056221e-22 4.36741892293e-22 4.35434229093e-22 4.28092903009e-22 4.29036338049e-22 4.3306875641e-22 4.31657825444e-22 4.3232907521e-22 4.32502137835e-22 4.32149564374e-22 4.32765523662e-22
Michigan - DENT - 520
Linear algebra a brief reviewStilian A. Stoev Lecture Notes for STAT 520 Fall 200611.1Matrix algebraBasic notions and operationsA triangular array A of scalars (here, real R or complex C numbers) is said to be a matrix. Notation: A = (aij )
Michigan - DENT - 614
1.1Integer Programming and Combinatorial OptimizationKatta G. Murty Lecture slides Integer Programming (IP) deals with LPs with additional constraints that some variables can only have values 0 or 1 integer values or values in some specied disc
Michigan - PIANO - 139
THE ORGANIZATION OF THE AMERICAN CITY IN THE LATE 19TH CENTURY: ETHNIC STRUCTURE AND SPATIAL ARRANGEMENT IN DETROIT*by0livi.er ZunzPaper written for a special issue of the Journal of Urban History, 'Immigrants and Workers in European and Americ
Michigan - PIANO - 340
Econ 340 Winter Term 2009 Study QuestionsAlan Deardorff Comparative Advantage Page 1 of 6Study Questions Lecture 3 Comparative Advantage and the Gains from Trade Part 1: Multiple ChoiceSelect the best answer of those given. 1. According to the t
Michigan - PIANO - 340
Econ 340 Winter Term 2009 Study Questions (with Answers)Alan Deardorff Comparative Advantage Page 1 of 6Study Questions (with Answers) Lecture 3 Comparative Advantage and the Gains from Trade Part 1: Multiple ChoiceSelect the best answer of thos
Michigan - PIANO - 439
THE CHORDAL ANALYSIS OF TONAL MUSICBRYAN PARDO WILLIAM P. BIRMINGHAMELECTRICAL ENGINEERING AND COMPUTER SCIENCE DEPARTMENT THE UNIVERSITY OF MICHIGAN MARCH 28, 2001 TECHNICAL REPORT CSE-TR-439-011KEYWORDSHeuristic Search, Music Analysis, Segme
Michigan - DENTED - 602
ANALYSIS O THE F NATIORAL CRASH SEVERITY STUDY DATAReport Number UM-HSRI-78-63James O'Day P h y l l i s Gimotty Richard Kaplan L i l y Huang Bruce Bertram Kenneth CampbellHighway S a f e t y Research I n s t i t u t e The U n i v e r s i t y of
Michigan - DENTED - 606
Heterosexual Cohabitation in the United States: Motives for Living Together among Young Men and Women*Pamela J. SmockDepartment of Sociology and Population Studies Center Institute for Social Research The University of Michigan Ann Arbor, MI 48106
Michigan - DENTED - 610
SPECIAL SECTIONAddress Entry While Driving: Speech Recognition Versus a Touch-Screen KeyboardOmer Tsimhoni, Daniel Smith, and Paul Green, University of Michigan Transportation Research Institute, Ann Arbor, MichiganA driving simulator experiment
Michigan - DENTED - 610
Chapter 5. 14. a) Let N1 , N2 be the numbers of Xi s such that Xi = 1 and Xi = 2 respectively. Let p = P(Xi = 1) and q = P(Xi = 2). Then, the probability function of (X1 , . . . , Xn ) is f (x1 , . . . , xn ) = (1 p q)nn1 n2 pn1 q n2 = exp{(n n1
Michigan - DENTED - 612
3.1Single Commodity Maximum Flow ProblemKatta G. Murty, IOE 612 Lecture slides 3Simple Transformations1. To get a model with a single source: If many souce nodes with specied availabilities, can introduce Supersource And convert problem into on
Michigan - DENTED - 612
REGRESSION UNDER SHAPE CONSTRAINTS IN A A FULL RANK EXPONENTIAL FAMILYMoulinath Banerjee The University of MichiganAbstractKey words and phrases:1IntroductionFunction estimation is a ubiquitous, and consequently wellstudied problem in nonp
Michigan - PMR - 510
PMR 510 Course Schedule/Topics* Readings are to be read BEFORE lecture session!DATE Sept. 5 Sept. 8 Sept. 12 Sept. 15 Sept. 19 Sept. 22 Sept. 26 Sept. 29 Oct. 3 Oct. 6 Oct. 10 Oct. 13 Oct. 17 Oct. 20 Oct. 24 Oct. 27 Oct. 31 Nov. 3 Nov. 7 Nov. 10 N
Michigan - POLISH - 314
ULWR - HULec T &amp; Th Lab M3 credits11:30AM1PM 7PM9PMPOLISH 314/SAC 441.003 Polish CinemaThe course covers Polish cinema from WWII to the present, tracing the development of lm styles and genres in the context of the historical, political, and
Michigan - POLISH - 422
-Center for Research on Social Organization The Working Paper Series The University of Michigan Ann ArborINTERNATIONAL CONFLICT AND THE INDIVIDUAL Helen WeingartenFaYA Working Paper # 22 CRSO Working Paper #422May 1990International Conflict
Michigan - POLISH - 432
WTRANSFORMATIONScomparative study of s o d transformationsCSST WORKING PAPERSThe University of MichiganAnn ArborCOLLECTIVE VIOLENCE AND COLLECTIVE LOYALTIES I N FRANCE: W Y THE H FRENCH REVOLUTION MADE A DIFFERENCE W i l l i a m H, Sewell, J
Michigan - POLISH - 450
&quot;Feeling History: Reflections On the Western Culture ControversynRenato Rosaldo CSST Working Paper #60 October 1990 CRSO Working Paper #450FEELING HISTORY: REFLECTIONS ON THE WESTERN CULTURE CONTROVERSY Renato Rosaldo Department of .Anthropology S
Michigan - POLISCI - 101
POLITICAL SCIENCE 101 INTRODUCTION TO POLITICAL THEORY: PERENNIAL QUESTIONS AND CLASSIC TEXTS Fall 2008 Professor Arlene W. Saxonhouse 7772 Haven Hall 764-6389 awsaxon@umich.edu Lecture MW 11:00, Aud B Angell Hall Office Hours: Tuesday 3:00-5:00 or b
Michigan - POLISCI - 302
.Movement and Countermovement: Loosely Coupled C o n f l i c tMayer N. Zald U n i v e r s i t y of Michigan B e r t Useem U n i v e r s i t y of I l l i n o i s a t Chicago C i r c l e October 1983..CRSO Working Paper 302Copies a v a i l a b
Michigan - POLISCI - 327
THE WEB OF POWER: Elites, Social Movements, and Structural Change, A Method of-AnalysisJeffrey P. BroadbentOctober, 1985I, IntroductionThe relation between macro-social structure and individual-level action is a central problem of sociology (G