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Space Charge Neutralization. Implications re pulsing or chopping the beam. TRIUMF 500 MeV cyclotron. 300 keV, < 1 mA injected beam (V sc < 1.2 volts) Space charge effect is small except near inflector We use all electrostatic optics: neutralization is very small.
Space Charge Effect. Up to now single particle longitudinal dynamics has been considered. In a real beam (or bunch), with many particles, each particle will suffer the repulsive forces from the others since they have the same electrical charge.
KINE 3301 Biomechanics of Human Movement. Linear Kinetics Reaction Forces. Chapter 7. Definitions. Kinetics : the study of forces and the motion they cause. Force : a force is a push or pull. Forces can be divided into: Contact forces Non-Contact force such a gravity.
Linear-Space Alignment. Subsequences and Substrings. Definition A string x’ is a substring of a string x, if x = ux’v for some prefix string u and suffix string v (similarly, x’ = x i …x j , for some 1 i j |x|) A string x’ is a subsequence of a string x
Linear-Space Alignment. Linear-space alignment. Using 2 columns of space, we can compute for k = 1…M, F(M/2, k), F r (M/2, N – k) PLUS the backpointers. x 1. …. x M/2. x M. x 1. …. x M/2+1. x M. y 1. y 1. …. …. y N. y N. Linear-space alignment.