The pivoting strategy of Bunch and Marcia for solving systems involving symmetric indefinite tridiagonal matrices uses two different methods for solving 2 × 2 systems when a 2 × 2 pivot is chosen. In this paper, we eliminate this need for two methods by adding another criterion for choosing a 1× 1 pivot. We demonstrate that all the results from the Bunch and Marcia pivoting strategy still hold....

KEKB is a double-ring energy-asymmetric electronpositron collider, now operating at KEK. In order to achieve a luminosity on the order of 1033=cm2=sor more, a very large number of bunches are stored. At present, the number of bunches is about 1,200 and the bunch spacing is 8 ns, in the usual physics operation. Consequently, strong coupled-bunch instabilities have been observed. In order to supp...

Electron cloud induces a transverse wake force which makes a correlation between bunch by bunch, namely a transverse displacement of a bunch causes a perturbation of electron cloud, which affects the transverse motion of following bunches. The correlation can be regard as a kind of wake force. We study the coupled bunch instability caused by electron cloud in drift space and in weak solenoid fi...

Longitudinal and transverse phase space information has been obtained from a statistical analysis of fluctuations in the radiation spectrum of an electron bunch. Uncorrelated shot noise fluctuations in longitudinal beam density result in incoherent radiation with a spectrum that consists of spikes, with width inversely proportional to the bunch length. Measurements were performed at l 620 nm on...

In the Fermilab Main Injector (MI) we are planning to double the bunch intensity from its design value by slip stacking. The accelerator consists of 18 rf cavities which operate at a harmonic number of 588. These cavities are known to have many higher ordered resonances. Longitudinal coupled-bunch instability induced by excitation of the rf cavities may be an important issue to be addressed in ...

The synchrotron light of the SLC damping ring was used to measure the bunch length with a streak camera at different times in the damping cycle. There are bunch length oscillations after injection, different equilibrium length during the cycle due to rf manipulations to avoid microwave instability oscillations, and just before extraction there is a longitudinal phase space rotation (bunch munch...

Plasma Wake-Field Acceleration (PWFA) has demonstrated acceleration gradients above 50 GeV/m. Simulations have shown drive/witness bunch configurations that yield small energy spreads in the accelerated witness bunch and high energy transfer efficiency from the drive bunch to the witness bunch, ranging from 30% for a Gaussian drive bunch to 95% for bunch with triangular shaped longitudinal prof...

A trigger bunch of electrons traveling inside or in the vicinity of a dielectric medium generates a Cerenkov wake. If the dielectric medium is active, a small fraction of the spectrum of the wake is amplified and far behind the trigger bunch where the active medium is fully depleted, the amplitude and the phase of the wake are virtually constant. In this range, a second bunch of electrons trail...