STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
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Since the remainder of this dissertation deals specifically with the properties of<br />
dipole HOMs, the subscripts will be dropped from the ratio (Rd/Qo) and will be<br />
quoted simply as (R/Q).<br />
4.5 BBU Simulation Codes: Eigenvalue Solutions<br />
While most existing BBU simulation codes are based on the particle tracking<br />
algorithm discussed in Section 4.3, a notable exception is the code M<strong>AT</strong>BBU (Matrix<br />
Beam Breakup).<br />
4.5.1 M<strong>AT</strong>BBU<br />
The simulation code M<strong>AT</strong>BBU developed at Jefferson Laboratory was used to<br />
predict the threshold currents in the IR FEL Demo as well as the FEL Upgrade<br />
Driver [73, 68]. Unlike its predecessor TDBBU, M<strong>AT</strong>BBU solves for the threshold<br />
current analytically, making use of the dispersion relation that exists between the<br />
beam current and frequency, Eq. (4.41) [26]. Numerically, solutions can be found by<br />
determining the current Io as a function of real Ω while scanning in frequency [72].<br />
At sufficiently high current the beam motion becomes unstable which is marked by<br />
the complex frequency having a positive imaginary part. The point at which this<br />
frequency intersects the real axis of the complex current plane gives the threshold<br />
current [69]. By sweeping the frequency, M<strong>AT</strong>BBU can locate these instabilities,<br />
specifying the frequency and current at which they occur. This process is illustrated<br />
in Fig. 4.4 which shows the results of scanning the frequency in the complex current<br />
plane. The lowest current to intersect the real current axis defines the threshold<br />
current and is shown in the inset figure.<br />
Because of its unique approach to predicting the threshold current, M<strong>AT</strong>BBU<br />
is able to determine the threshold current corresponding to many individual modes.<br />
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