A METHOD TO TUNE PULSE MAGNETS ' WAVEFORMS
9th Int Particle Accelerator Conf (IPAC'18), Vancouver, BC, Canada, April 29-May 4, 2018(2018)
Abstract
Pulse magnets are used in storage ring injection kickers. The waveform of the four kickers have strong relation with injection efficiency. A slightly offset of waveform may cause the four kickers mismatched, which would lead to storage beam loss and decrease injection efficiency. In order to define the peak value and timing of the half-sine waveform which has noises interfering diagnosis, a curve-fitting method was introduced to monitor and fine-tuning the waveform. The waveforms' data are also archived for reference in case of replacing power supplies. By using this method, it helps to retain a consistent injection efficiency after the power supplies maintenance or replacement. INTRODUCTION The accelerator complex of Taiwan Photon Source (TPS) project consists of a 150 MeV linac, 3 GeV booster, and a 3 GeV storage ring. Pulsed magnets are used for beam injection into and extraction out of the booster and storage ring. The layout of TPS injection scheme and its associated geometric arrangement are illustrated in Fig. 1. There are three septum power supplies with the same configuration and four identical units of kicker fabricated for TPS project [1]. It’s crucial to match shape of these kickers’ waveforms for top-up operation or it will inhibit users from data acquisition application. The power supplies would degrade with time or sometimes broke down for replacement. To ensure the consistent performance of the kickers and septum, the peak values of the half-sine waveforms were introduced as an indicator to tune and monitor them. However, due to the alias of the waveform, a curve-fitting method was implemented to pinpoint the peak values. Figure 1: Layout of TPS injection scheme and the related parameters. KICKER & SEPTUM POWER SUPPLY To guide the electron beam aiming toward the designated space coordinates and arriving at the proper entrance of the transfer line, the septum are arranged at upstream of injection kicker and downstream of extraction kicker. The half-sine pulses of the kickers are illustrated in Fig. 2. In real situations, the pulses are not perfect half-sine curves. Once the pulses were inspected in a small scale or zoomed in, the noises and alias of the signals inhibit us from determining the peak values of the pulses (Fig. 2 and 3). To analyse the signals, we use MATLAB curve-fitting tool to find curves which have the smallest SSE (Error Sum of Squares) with the original data. The peak position values were then determined as an indicator to tune the pulses. Figure 2: The aligned pulses of four units kicker power supplies. Figure 3: Zoom into the black square area of Fig. 2. CURVE-FITTING TOOL Since the pulses are designed as half sine, ‘Sum of Sine functions’ model was firstly put into tested. The sum of sines model fits periodic functions, and is given by: . ( ) = ∗ sin( ) Ā ⋯ sin( ) (1) where a is the amplitude, b is the frequency, and c is the phase constant for each sine wave term. n is the number of terms in the series and 1 ≤ n ≤ 8. This equation is closely related to the Fourier series described in Fourier Series. The main difference is that the sum of sines equa9th International Particle Accelerator Conference IPAC2018, Vancouver, BC, Canada JACoW Publishing ISBN: 978-3-95450-184-7 doi:10.18429/JACoW-IPAC2018-WEPAL063 WEPAL063 2320 Co nt en tf ro m th is w or k m ay be us ed un de rt he te rm so ft he CC BY 3. 0 lic en ce (© 20 18 ). A ny di str ib ut io n of th is w or k m us tm ai nt ai n at tri bu tio n to th e au th or (s ), tit le of th e w or k, pu bl ish er ,a nd D O I. 06 Beam Instrumentation, Controls, Feedback, and Operational Aspects T03 Beam Diagnostics and Instrumentation tion includes the phase constant, and does not include a constant (intercept) term. The fitting results (Fig. 4) shows that the goodness of fit changes with n. There are four factors to determine the goodness of fit: [2] The sum of squares due to error (SSE) R-square Adjusted R-square Root mean squared error (RMSE) Figure 4: Fitting results of different number of terms n=1~4. Table 1: Goodness of fit with Different Number of Terms n SSE R-square Adj. Rsquare RMSE n=1 1.8*105 0.524 0.523 4.264 n=2 1.1*104 0.971 0.970 1.063 n=3 3322 0.9913 0.9913 0.5766 n=4 3295 0.9914 0.9914 0.5744 Sum of Squares Due to Error(SSE) This statistic measures the total deviation of the response values from the fit to the response values. It is also called the summed square of residuals and is usually labeled as SSE.
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