Electrostatic Propulsion with Highly Charged Microparticles

Electrostatic Propulsion with Highly Charged Microparticles Thomas Trottenberg∗and Holger Kersten Institut f¨ur Experimentelle und Angewandte Physik, Christian-Albrechts-Universit¨at Kiel, D-24098 Kiel, Germany Horst Neumann Leibniz-Institut f¨ur Oberfl¨achenmodifizierung, D-04318 Leipzig, Germany 5th International Spacecraft Propulsion Conference, May 5th - 8th, 2008, Heraklion, Crete, Greece Abstract — A novel electrostatic propulsion concept is proposed which uses conductive microparticles as propellant. The particles are to be charged positively by contact with needle electrodes at high electrostatic potential (∼+20 kV). This technique allows the maximum possible charges on microparticles, which are limited by Coulomb fragmentation and field evaporation. Introduction Electrostatic propulsion has, in comparison with chemical and electrothermal propulsion, the advantage, that very high exhaust speeds can be attained. The exhaust speed is an important parameter, because it determines, how much propellant is needed for a desired change of the momentum of the space vehicle. The produced momentum piper ion mass miis identical with the the speed vi=pi/mi(“specific impulse”). Electrostatic propulsion is still a synonym for ion thrusters, but in principle also molecules, clusters, nanoand microparticles could be accelerated by electrostatic forces. Such alternative concepts are still in the stage of prelimi- ∗email: [email protected] nary investigations. Examples are field emission thrusters which are operated in the iondroplet mixed regime (colloid thrusters) [1], and nanoparticle thrusters, which extract charged particles from a suspension by means of electric fields [2]. In this contribution, we consider the possibility of a novel thruster concept which uses solid metal or conductively coated dielectric microparticles as propellant. First, the charging technique for fine particles is described, and the achievable charge-to-mass ratio (specific charge) qp/mpis estimated. Besides the accelerating potential Uacc, the specific charge is the decisive parameter for the exhaust velocity vp0 of the particles and the specific impulse Isp =vp0/g. Second, the acceleration and the attainable specific impulses are considered. Third, we discuss the choice of the particle material. Charging and Acceleration of Microparticles Charging Technique Hypervelocity experiments for the simulation of micrometeorites and their impacts for example on the surface of the moon, space vehicles, spacesuits and instruments also use electrostatic 1 mpvp0 2rpqp/mpqpEp material [kg] [km s−1] [µm] [C kg−1] [e] [V m−1] iron 10 ×10−16 4 0.62 +4.0 +25 000 0.4×109 iron 10 ×10−16 10 0.62 +25 +160 000 2.3×109 latex 2.4×10−16 5 0.75 +6.3 +9 400 0.1×109 latex 2.4×10−16 11 0.75 +30 +45 000 0.5×109 Tab. 1: Experimental parameters. Mass mpand speed vp0 were selected from speed-mass distributions of about 20 000 iron and 2840 latex particles published in [4], the other parameters were calculated. The particles were accelerated with a potential of Uacc = 2 MV. acceleration of charged microparticles. A successful technique applied there allows the highest possible specific charges (see below). The particles are charged by contact with very small spherical or needle-shaped surfaces at high voltage potentials, as indicated in Fig. 1(a). Shelton et al. [3] applied this technique using as charging electrode a tapered tungsten wire with a diameter of 2rn= 24 µm at the tip, which is maintained at a positive potential of Un= +20 kV. When a microparticle (rp< rn) touches the (spherical) needle tip , it acquires the charge qp=2 3π3ǫ0rn r2 p (rp+rn)2Un.(1) With the assumption rn≫rp, the electric field strength on the particle becomes Ep= π2Un/6rnafter separation from the electrode. For example a needle tip with radius rn= 12 µm at a potential of Un= +20 kV yields an electric field strength of Ep= 2.7×109Vm−1. A 1-µm iron particle (ρ= 7874 kg m−3) would carry 475 000 positive elementary charges and have a specific charge of qp/mp= +18.5 C kg−1. The values for the smaller 100-nm particle are qp= +4750eand qp/mp= +185 C kg−1. Of course, this ratio is much less than for a singlycharged xenon ion (7.3×105C kg−1). Dielectric particles can also be charged with this technique, but they have to be coated with a conducting material. In the Heidelberg Dust Accelerator coated latex particles were successfully used [4]. Table 1 shows some of the experimental values for iron and latex particles. The latex particles had a narrow size distribution centered about 0.75 µm, and most of the particles were accelerated to speeds between 5 and 11 km s−1. The size distribution of the iron powder was broad (0.2−2.4µm) resulting in speeds from less than 1 km s−1to more than 10 km s−1. Fig. 1: (a) Schematic of particle charging and acceleration. The particle P is charged at the needle N, is accelerated towards the electrode E, and leaves the system through the hole in the electrode. (b) Expected specific charge for iron particles (24-µm needle tip at ±20 kV). Dashed lines show the limits for electron field emission (lower line) and field evaporation (upper line). Upper Limits for the Particle Charge The electric charge on a microparticle is limited by two processes which become important at very high electric field strength on the particle surface [5]. For negative charges electron 2 ρ2rp= 1.0µm 2rp= 0.1µm material kg m−3C kg−1C kg−1 latex 1100 (−48 ...+ 480) (−480 ...+ 4800) MF 1500 (−35 ...+ 350) (−350 ...+ 3500) aluminum 2700 (−20 ...+ 200) (−200 ...+ 2000) iron 7874 (−6.7...+ 67) (−67 ...+ 670) Tab. 2: Estimated range of the possible specific charges for spherical particles with different materials and sizes. The critical electric field strengths have been assumed cautiously to be 109V m−1for negative and 1010 V m−1for positive charges [5]. field emission begins at |Ep|>109V m−1. For positive charges field evaporation destroys the particle, if |Ep|>1010 V m−1. In case of materials with low tensile strength or fluffy grains, charges of both signs are able to fragment the particles (“Coulomb explosion”) [6] already at lower field strengths. The specific charge qp/mp, which is the crucial parameter for electrostatic acceleration, can be related to the electric field at the surface Ep=qp/4πǫ0r2 p, assuming spherical particles. By means of the particle mass mp=4 3πr3 pρ, one obtains the specific charge as qp mp = 3ǫ0Ep rpρ.(2) This equation can be used to calculate the maximum possible specific charge, which depends on the particle size and density and the critical electric field strengths for positive and negative charges. Table 2 shows the charge-to-mass ratios for some combinations of size and material assuming that the above mentioned critical field strengths are the same for all the particles and that the particles are spheres. Figure 1(b) shows the expected charge-tomass ratios for the contact-charging technique. In case of iron particles charged by contact with a 20-kV needle, electron field emission would limit negative charging, meanwhile positively charged particles are not yet affected by field evaporation. For this reason only positive charging potentials should be applied. Acceleration of Charged Microparticles In order to make the particles useful for propulsion, they have to be accelerated by an electric field. The desired specific impulse determines the required acceleration voltage Uacc by means of the equation 1 2mpv2 p0 =|Uaccqp|.(3) When the particles leave the dust source, they have already been accelerated by the potential difference between the needle and hole electrode. In case of the Heidelberg Dust Accelerator [4], a subsequent acceleration with 20 kV or 2 MV was accomplished, but this is not necessary. In Table 3 the performance of the particle source without and with an additional accelerating system is shown. The source alone surpasses cold gas thrusters in specific impulse, and with a further 180-kV acceleration the microparticle thruster becomes comparable with chemical thrusters. Accelerating potentials in the range of 105V should technically not be a problem [7]. material iron latex mp[10−16 kg] 10 2.4 2rp[µm] 0.62 0.75 qp/mp[C kg−1] +25 +30 Isp [s] at Uacc = 20 kV 100 110 Isp [s] at Uacc = 200 kV 316 346 Tab. 3: Expected specific impulses. The chargeto-mass ratios are the same as in Table 1. 3 Propellant Material Spherical Particles Microparticles made of melamine, silica and other materials are available with nearly perfect spherical shape, narrow size distributions and optional metal coatings [8]. Spherical particles are advantageous with respect to charging and handling for the following reasons. The contact-charging technique allows particle charges close to the theoretical limits defined by electron field emission and field evaporation. These limits are highest for spherical particles, because there the charges are uniformly distributed over the surface. If the shape deviates from a sphere, the charge density and consequently the field strength decrease on some parts of the surface and increase on others. In the high field regions, especially at sharp edges, field emission and evaporation would occur at lower particle charges. For this reason spherical particles are to be preferred. Moreover, monodisperse spherical particles are easier to handle. From the authors’ experience, dry melamine formaldehyde (MF) particles with at least 0.5 µm diameter do not clump and behave in a container like a liquid. Amorphous powder particles with a broad size distribution tend much more to clog. This effect is known from granular materials as “jamming” [9]. However, the smaller the particles are, the more important become the cohesive forces as an additional effect, so that also spherical particles agglomerate. For this reason manufacturers of monodisperse microparticles deliver particles smaller than 500 nm in aqueous suspensions [8]. On-board Synthesized Particles Particle formation in reactive and etching plasmas, e.g. with methane, silane and acetylene, are well known [10] so that one can think about the production of particles on board. The generation of the plasma where the particles are formed consumes additional energy which debits the efficiency of the thruster and causes additional weight for the plasma reactor and necessary electronics. But there are also some advantages over prefabricated particles, e.g. clumping of stored particles and congestion of tank and ducts as possible troubles would be avoided. However, the authors think that it is untimely to discuss the concept of on-board production in detail before a thruster works with well-defined model particles. Hollow Particles Hollow glass microspheres (“microballoons”) are known as a low-priced filler in composite materials like epoxy resin and light weight concrete1. Such particles have nearly perfect spherical shape and very thin walls, which are approximately 300 nm thick. The lower over-all mass density of a hollow microparticle can yield higher specific charges. First, we consider the maximum possible specific charge limited by the field strength Ep,max corresponding to one of the two effects discussed above. Similarly to Eq. (2) the charge-to-mass ratio can be recalculated for a hollow sphere with radius rp,h, wall thickness dp≪rp,h, material density ρhand the particle mass mp,h= 4πr2 p,hdpρh: qp,h mp,h =ǫ0Ep,max dpρh .(4) It is noteworthy that the charge-to-mass ratio does not depend on the particle radius rp,h, and it is now the wall thickness dpwhich determines the specific charge. A comparison of Eq. (2) with Eq. (4) for a filled sphere with radius rp,f and density ρfresults in a higher specific charge for a hollow sphere, if dp<(1/3)(ρf/ρh)rp,f. A hollow glass microsphere with 300-nm walls and arbitrary radius has therefore only a better charge-to-mass ratio than a glass pearl bigger than 1.8 µm. But hollow microspheres made of another material and with a modified method of production might have even thinner walls and be better suited as propellant. Second, we consider the specific charge of the hollow sphere for a given surface potential φp,h. This is the situation, when the field 1Scotchlite S22, 3M Deutschland GmbH 4 strength limits are not reached. Using qp,h= 4πǫ0rp,hφp,h, one obtains the specific charge of the hollow sphere qp,h mp,h =ǫ0φp,h dprp,hρh .(5) For comparison, the filled sphere has the chargeto-mass ratio qp,f mp,f = 3ǫ0φp,f r2 p,fρf .(6) The hollow sphere has a higher specific charge, if dprp,h<(1/3)(ρf/ρh)r2 p,f. The hollow microspheres with 300-nm walls have therefore no significant advantage over a massive particle with 2rp,f≈1µm in this case. Conclusion An electrostatic microparticle thruster, which uses high voltage needle electrodes to charge conducting particles positively, seems to be feasible. This technique is known from accelerators for the simulation of micrometeorites. Charging and acceleration are both done in one small electrode assembly. The concept allows highest specific charges, which are only limited by field evaporation and Coulomb explosion in case of fluffy grains. It has been shown, that acceleration voltages in the range of 105V yield exhaust velocities comparable to chemical thrusters. While the existing dust accelerators are not optimized for high ejection rates, a thruster would probably use a miniaturized needle array instead of a single needle electrode in order to obtain a continuous particle beam. A possible application will depend on the specific impulse, the thrust level and the efficiency. It is still too early to answer these questions before experiments on a reliable contact charging with high repetition rate have been performed. The authors plan preliminary experiments for the near future. Acknowledgments This work is supported by the German Aerospace Center DLR, Projects No. 50 JR 0644 and No. 50 RS 0802. References [1] P. Lozano and M. Mart´ınez-S´anchez. Studies on the Ion-Droplet Mixed Regime in Colloid Thrusters. PhD thesis, MIT, Department of Aeronautics and Astronautics, 2003. [2] L. Musinski, T. Liu, B. Gilchrist, A. Gallimore, and. M. Keidar. Proceedings of the International Electric Propulsion Conference, IEPC-2005-176, 2005. [3] H. Shelton, C. D. Hendricks Jr., and R. F. Wuerker. J. Appl. Phys. 31 1243, 1960. [4] M. St¨ubig, G. Sch¨afer, T.-M. Ho, R. Srama, and E. Gr¨un. Planet. Space Sci. 49 853, 2001. [5] E. W. M¨uller. Phys. Rev. 102 618, 1956. [6] J. Svestka, I. Cermak, and E. Gr¨un. Adv. Space Res. 13 199, 1993. [7] R. G. Jahn. Physics of Electric Propulsion. McGraw-Hill, 1968. [8] Microparticles GmbH, Berlin, http:\\www.microparticles.de. [9] J. Duran. Sands, Powders, and Grains: An Introduction to the Physics of Granular Materials. Springer, 2000. [10] Ch. Hollenstein. Plasma Phys. Control. Fusion 42 R93, 2000. 5