Energy loss due to eddy current in linear transformer driver cores

Abstract

In linear transformer drivers [Phys. Rev. ST Accel. Beams 12, 050402 (2009); Phys. Rev. ST Accel. Beams 12, 050401 (2009)] as well as any other linear induction accelerator cavities, ferromagnetic cores are used to prevent the current from flowing along the induction cavity walls which are in parallel with the load. But if the core is made of conductive material, the applied voltage pulse generates the eddy current in the core itself which heats the core and therefore also reduces the overall linear transformer driver (LTD) efficiency. The energy loss due to generation of the eddy current in the cores depends on the specific resistivity of the core material, the design of the core, as well as on the distribution of the eddy current in the core tape during the remagnetizing process. In this paper we investigate how the eddy current is distributed in a core tape with an arbitrary shape hysteresis loop. Our model is based on the textbook knowledge related to the eddy current generation in ferromagnetics with rectangular hysteresis loop, and in usual conductors. For the reader's convenience, we reproduce some most important details of this knowledge in our paper. The model predicts that the same core would behave differently depending on how fast the applied voltage pulse is: in the high frequency limit, the equivalent resistance of the core reduces during the pulse whereas in the low frequency limit it is constant. An important inference is that the energy loss due to the eddy current generation can be reduced by increasing the cross section of the core over the minimum value which is required to avoid its saturation. The conclusions of the model are confirmed with experimental observations presented at the end of the paper.

Square pulse linear transformer driver

“…The cavity core is made of ET3425 iron tape with the thickness ¼ 80 m, and the length of its center line [6] (here is equal to the length of the core mean circumference) is ' $ 1:2 m. It consists of 6 rings, the total cross section of iron in these rings being S $ 53 cm 2 . At passive premagnetization [6], which was used in tests described below, the volt-second integral of this core is VS CORE $ 17 mV s.…”

Force on a storage ring vacuum chamber after sudden turn-off of a magnet power supply

“…Eddy current will arise when the magnets are excited with harmonic or transient current. Harmonic excitations of magnets are required for boosters or rapid cycling synchrotrons, often used as injectors for large machines storing a charged particle circulating beam, and operated in the persistent mode, which are studied in detail and reported earlier by others including ourselves [1][2][3]. However, the effect of exponential decay of field has not been studied.…”

“…If the magnets produce a time varying field then it will generate an eddy current in the vacuum chamber which in turn modifies the B field produced by the accelerator magnets. That can cause disturbance to the circulating beam [1][2][3]. Beam position monitors (BPMs) are mounted at vacuum chambers to detect the position of the particle beam.…”

Impedance-matched Marx generators

“…A linear-transformer-driver (LTD) module is an induction voltage adder that is powered by circuits located within the cavities of the adder [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Since an LTD module can be designed to provide single-stage electrical-pulse compression and impedance matching, such modules are attractive candidates as prime-power sources for nextgeneration pulsed-power accelerators .…”

“…For each cavity, Fig. 3 models the cores as a resistive circuit element with resistance R cores located at the cavity output [7,13,[15][16][17][18][19][20].…”