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• W2766161505 abstract "Accepted for Publication in Physica C (2009) MICE Note 259 Over Voltage in a Multi-Sectioned Solenoid during Quenching X. L. Guo, F. Y. Xu, L. Wang, M. A. Green, H. Pan, H. Wu, X. K. Liu, and A. B. Chen The second method divides the coil into segments and deciding the state of each segment based on the propagation velocity [7-9]. This method can solve the voltage distribution along the wire if the segments are along the wire, but the temperature solving by this method needs a larger computing effort than that by the first method [8]. The third method is based on treating the coil as an anisotropic solid and solving the nonlinear heat differential equations governing the quench process [10-15]. This method can solve the voltage distribution in the coil, but it needs a larger computing effort than even second method [10], [12]. To the authors’ knowledge, the first one method is more diffused than the other two methods, because it is very fast and gives globally correct results. However, there is little attention to the voltage distribution and detailed over voltage analysis by the first method. This paper is mainly devoted to the over voltage analysis within the solenoid using the first method of analysis. Based on the classic assumption of an ellipsoid normal zone, three- dimension temperature results are mapped to one-dimension along the wire. The temperature distribution and the resistance distribution along the wire are obtained. The coil is treated as turn elements connected in series, and each turn element is a combination of resistance and inductances. The resistive voltage distribution and inductance voltage distribution and the resultant voltage of these two opposite voltages distribution are obtained. The maximum internal voltage, the layer-to-layer voltage and the turn-to-turn voltage during quenching are estimated. The method in this paper can make the over voltage calculation by the first method more accurate. I. M ODELING OF QUENCH PROPAGATION Based on the classical quench model, the normal zone in the space can be approximated as an ellipsoid. This ellipsoid spreads in three directions with different velocities until the entire magnet becomes normal. After each time step a layer is added to the normal zone – like the skins of an onion. Longitudinal propagation velocity v l and transverse propagation velocity v t can be calculated by the following equations [5]: v l = J ( γ C ) avm LT s T s − T 0 k t ⋅ v l = α ⋅ v l k l A b s t r a c t —Accurate analysis of over voltage in the superconducting solenoid during a quench is one of the bases for quench protection system design. Classical quench simulation methods can only give rough estimation of the over voltage within a magnet coil. In this paper, for multi-sectioned superconducting solenoid, based on the classical assumption of ellipsoidal normal zone, three-dimension al temperature results are mapped to the one-dimension of the wire, the temperature distribution along the wire and the resistances of each turn are obtained. The coil is treated as circuit comprised of turn resistances, turn self and mutual inductances. The turn resistive voltage, turn inductive voltage, and turn resultant voltage along the wire are calculated. As a result, maximum internal voltages, the layer-to-layer voltages and the turn-to-turn voltages are better estimated. Utilizing this method, the over voltage of a small solenoid and a large solenoid during quenching have been studied. The result shows that this method can well improve the over voltage estimate, especially when the coil is larger. Index Terms—Superconducting magnets, Over voltage, Quench Simulation, Quench Protection I. I NTRODUCTION UENCHING of a superconducting magnet can induce overheating, over-voltages, and in extreme cases destruction the magnet, so it is necessary to simulate the quench characteristics of superconducting magnet systems. Overheating can be better estimated by using the time varying currents and the resistance of the normal zone within the coil. Estimating over voltage requires an understanding of the voltage distribution along the wire [1], [2]. There are three types of quench simulation methods. The first method calculates the normal zone shape in the coil based on propagation velocities in three dimensions. Using this method, some codes calculate the terminal voltage [3], [4]. Other codes calculate the voltage drop on only the resistance of the normal zone [5], [6], and yet other codes calculate the voltage distribution in the coil assuming the inductance of every layer is the same [2]. Q This work was supported by funds of the cryogenic and technology innovation project under the “985-2” plan of Harbin Institute of Technology. This work was also supported by the Office of Science US Department of Energy under DOE contract DE-AC02-05CH11231. X. L. Guo, F. Y. Xu, L. Wang, H. Pan, H. Wu, X. K. Liu and A. B. Chen are with the Institute of Cryogenics and Superconductive Technology, Harbin Institute of Technology, Harbin 150001, China (e-mail: guoxinglong@hit.edu.cn ). M. A. Green is with Lawrence Berkeley National Laboratory, Berkeley, CA 94720 USA (e-mail: magreen@lbl.gov). (1a) v t = ( γ C ) avm ( γ C ) av (1b)" @default.
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