Publication Title | ADVANCES IN APPLIED PLASMA SCIENCE 2011

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Text | ADVANCES IN APPLIED PLASMA SCIENCE 2011 | 005 A two-grid-system test stand will be built at IRS in order to understand the basics of confinement and plasma beam extraction. A grid design study has been conducted in order to obtain the most adequate setup for a test campaign that is supposed to deliver knowledge about the confinement process within the cathode grid and certain operation conditions e.g. the star mode. In a second test sequence a plasma beam extraction shall be established and examined with Langmuir probes and LIF measurements in order to obtain information about electron and ion properties. 6. Mini-magnetospheric plasma propulsion system Mini-magnetospheric plasma propulsion (M2P2) is a con- cept with low demand of propellant. This is a consequence of using solar wind to create thrust. The idea is based on the magnetic sail concept [35]: Coils generate a magnetic field around a space craft. Charged solar wind particles interact with the field according to the Lorentz force (7) where q is the particle charge, v is the particle velocity r and B the coil produced magnetic induction. Thus, the charged particles are deflected and produce a momentum transfer to the magnetosphere and finally to the space craft. This final momentum transfer depends on the magnitude of the interaction cross section between the magnetic field and the particles. The biggest problem of this concept is that a coil with a very large diameter of several km and a current of several kA are essential to produce a non- negligible momentum transfer to the magnetosphere. It was therefore proposed to inject plasma into the field [35], causing an inflation of the magnetic bubble (fig. 11), explainable with the MHD induction eq. (10). Figure 11: Schematics of the magnetic sail with plasma injection and enlarged magnetosphere limited experimental research focuses on the change of a magnetic field after the injection of the plasma [38, 39]. Thus, numerical simulation is essential for M2P2 studies. There are currently two main concepts for simulating the M2P2 system. The first is an MHD approach used in [36], the second proposed in [37] is a hybrid one joining MHD and kinetic equations. Results in thrust and size differ of six orders of magnitude between the two approaches making statements about an eventual practical use of M2P2 extremely difficult. The reason for the differences are the different spatial scales of the underlying model spanning from a few centimeters up to approximately 50 km, which is a great numerical difficulty. On one hand the MHD approach is not valid for all required scales on the other hand the coupling in a hybrid approach is difficult and the kinetic approach is a great computational effort. Despite the latter we want to discuss the application of a fully kinetic approach to obtain data on M2P2. The funda- mental equation is the gas kinetic Boltzmann equation: rr r FLor =qv×B r (9) is the single particle distribution function at rrr Advanced Plasma (Propulsion) Concepts at IRS r rr ∂r∂F∂rr ∂f(x,v,t) + v r + r f (x,v,t)= ∂t ∂x m∂v ∂t Here, rr coll f (x,v,t) The MHD induction equation r In [41], solvers and numerical requirements for the fully kinetic approach currently studied at the IRS are discussed. REFERENCES [1] Shepherd, D.; Aerospace Propulsion, American Elsevier Publishing Company Inc. New York, London, Amsterdam, 1972. [2] Herdrich G., Boxberger A., Petkow D., Gabrielli R., Fasoulas S.; 46th AIAA ASME/SAE/ASEE Joint Propulsion Conference, 2010, AIAA 2010-6531. [3] Haag, D., Auweter-Kurtz M., Fertig M., Herdrich G.; Trans. JSASS Space Tech. Japan, Vol. 7, No. ists26, pp. Tb_19-Tb_28, 2009 [4] Gay, S.A., Schmiegel, N.A.; FalconSAT-3 and the Space Environment, AIAA 2010-182, 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, Florida, January 4-7, 2010. [5] Kakami, A., Koizumi, K., Komurasaki, K., and Arakawa, Y.; Design and Performance of a Pulsed Plasma Thruster with ∂B r r 1 r −∇×(v×B)= ∆B ∂t σμ0 (σ: electric conductivity, μ0 magnetic constant) is valid in the vicinity of the plasma source, this means the conse- r quence according equation (10) is a change in B resulting in the discussed enlargement of the magnetosphere. Thus, the proportionality changes from B ∝ 1⁄r3 (r: distance) to B ∝ 1⁄rk | k < 3 with the decrease parameter k. According to recent theoretical studies the enlarged magnetosphere measures 20 [36] to 80 km [37]. This huge diameter is the problem for experiments of M2P2. Only (8) location x , at time t, with velocity v . Furthermore, F is an external force and m is the mass of the particles. The term on the right-hand side is called the collision term to describe the collision effects between particles. This term causes the great mathematical effort in solving the Boltz- mann equation [36]. For M2P2, the equation can be divided into two parts. The first part is the non-collisional long term interactions, they are describing the plasma behaviour dominated by collective plasma phenomena and neglecting the coulomb collisions, described mathema- tically by the Vlasov equation. A widely used approach for solving it is the PIC method. The second part is the collisional long range interactions, the Coulomb collisions which cannot be neglected for small spatial scales, i.e. at the plasma injection region. In such a case one has to solve the Fokker-Planck equation. An example for a highly efficient method for solving it was developed in [40]. 5 | Image | ADVANCES IN APPLIED PLASMA SCIENCE 2011 |

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