The Cockcroft Institute
Post-graduate
Lecture Courses: Academic Year 2005-6
Core Course
Fundamentals of
Wakefields and Impedance: From Physical-Mathematical Analysis to
Practical Applications (timetable)
Tutor : Dr RM Jones
This course will address
the fundamentals of wakefields and their relation to the beam
impedance. The features of both long-range and short-range wakefields
will be discussed. Circuit models of relativistic electron beams
coupled to multiple accelerator cavities will be developed in order to
facilitate the calculation of coupled modal frequencies and wakefields.
In addition to the general theoretical formalism of wakefields,
practical methods to damp and measure the wakefields will be described
with techniques taken from ongoing research on high-energy linacs
(L-band and X-band linacs in particular). Throughout the course, basic
physical principles such as superposition, energy conservation and
causality will be emphasized. The purpose of the course is to enable
students to become well-versed in the beam dynamics of wakefield-beam
interaction in high energy accelerators.
Syllabus
1. Part I of Fundamentals of wakefields and impedance.
Basic concepts and definitions are
introduced. A field function analysis of wakefields is discussed and
practical simplifications are introduced. The features of short-range
and long-range wakefields are sketched out.
2. Part II of Fundamentals of wakefields and impedance and applications
to linear colliders.
Further general features of wakefields
are described. The wakefield issues that are likely to arise in
any high current low-emittance accelerator are analysed. In
particular, the wakefield in both L-band (superconducting) and X-band
(normalconducting) linacs are investigated. Mode coupling issues that
are likely to arise in the ILC main superconducting linacs are
described. A circuit model of the dipole wakefield is developed
for moderate to heavily damped accelerator structures. Interleaving the
cell frequencies of adjacent structures is introduced as a means to
combat insufficient fall-off in wakefields. Manifold damped structures
are modeled with a transmission-line combined with an L-C circuit model
and the additional features (built-in BPM and structure alignment
thorough monitoring of manifold radiation) of DDS (Damped Detuned
Structures) are modelled in detail.
3. Special topics: Detailed study of resistive wall wake. BBU (Beam
BreakUp). Impedance and wakefields issues in circular
accelerators are addressed.
4. Impedance and wakefield via a bench measurement.
Higher modes of the TESLA accelerator
and measurements made at the TTF (TESLA Test Facility). A coaxial
wire method, for determining the modes likely to be excited by a
particle beam, is described, from its original concept through to the
latest research.
Return to education page