Compensation for longitudinal space charge forces as inductive wall impedances

In particle accelerators and storage rings the longitudinal coupling impedance between the beam and its environment arises from the longitudinal space charge forces and the vacuum chamber component impedance. A scheme is considered for compensating the total longitudinal coupling impedance within a restricted frequency range. For the low-β case, when the net longitudinal impedance is a negative inductance, compensation is achieved by means of adding either passive inductive wall elements or actively excited inductive elements. In the latter case, the excitation is by current pulses which exactly simulate amplified beam current pulses, in shape and sign. For the high-γ case, when the net longitudinal impedance is a positive inductance, an active inductance wall element is again introduced but the exciting signal is reversed in sign from the previous case