By S. Y. Lee

Study and improvement of excessive strength accelerators started in 1911.

(1) improvement of excessive gradient dc and rf accelerators,

(2) fulfillment of excessive box magnets with very good box quality,

(3) discovery of transverse and longitudinal beam focusing principles,

(4) invention of excessive strength rf sources,

(5) development of ultra-high vacuum technology,

(6) attainment of excessive brightness (polarized/unpolarized) electron/ionsources,

(7) development of beam dynamics and beam manipulation schemes, resembling beam injection, accumulation, gradual and quick extraction, beam damping and beam cooling, instability suggestions, laser-beam interplay and harvesting instability for prime brilliance coherent photon source.

The affects of the accelerator improvement are evidenced by way of the numerous ground-breaking discoveries in particle and nuclear physics, atomic and molecular physics, condensed subject physics, biology, biomedical physics, nuclear drugs, clinical remedy, and business processing. This ebook is meant for use as a graduate or senior undergraduate textbook in accelerator physics and technology. it may be used as preparatory direction fabric in graduate accelerator physics thesis learn. The textual content covers old accelerator improvement, transverse betatron movement, synchrotron movement, an advent to linear accelerators, and synchrotron radiation phenomena in low emittance electron garage jewelry, creation to big issues resembling the loose electron laser and the beam-beam interplay. consciousness is paid to derivation of the action-angle variables of the part house, as the transformation is necessary for realizing complicated issues akin to the collective instability and nonlinear beam dynamics. each one part is by means of workouts, that are designed to enhance innovations and to resolve reasonable accelerator layout difficulties.

Readership: Accelerator, high-energy, nuclear, plasma and utilized physicists.

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3. Inside the vacuum chamber of an accelerator, we have V x 6 = 0 and V x E' = 0. xhus the electfic field and magnetic field can be expanded by scalar potentials with B = -V@,,E = -V@,, where both scalar potentials satisfy the Laplace equation with V2@, where @ stands for either a, or aPe = 0. In the curvilinear coordinates (2, s,z ) , we then have a9 l a VZ@ = -([l+hz]-) 1 +hxaz ax a2a 1 a (--) 1 a+ +4- -az2 1 + h z a S i + h z as = 0, where h = l f p , and p is the radius of curvature. Expressing the scalar potential in power series of particle coordinates, show that A,j satisfies the following iteration relation: CHAPTER 2.

10) CHAPTER 2. TRANSVERSE MOTION 32 where P‘ is the momentum in the Cartesian coordinate system. The conjugate momenta for the coordinates (5,s, z ) are (see Appendix A) aF, dF3 p s -- -- = (1 + x / p ) P . 2. 3, If2 , A’ in Eq. e. A, = 2 . 2 , A, = A . 2 . 13) A’ Note that A, and p , are not simply the projections of vectors and @ i n the d direction. In the new coordinate system, Hamilton’s equation becomes * aH . d H as ’ dH x. d H dx ’ . dH . z = -,pz dP, = _ d_H dz . 14) The next step is to use s as the independent variable instead of time t [15].

35 3. Consider a uniform cylindrical beam with N particles per unit length in a beam of radius a; show that a test charged particle traveling along at the same velocity as the beam, v, experiences a repulsive space-charge force, where y = l / d m and e is the charge of the beam particle. (a) Estimate the space-charge force for the SSC low energy booster at injection with kinetic energy 800 MeV and NB = 10" particles per bunch, with rms bunch length sS = 2 m and beam diameter 4 mm. Here the number of particles per unit length is N = N8/(&oS).