A code library BEAMPATH for 2-dimensional and 3-dimensional space charge dominated beam dynamics study in linear particle accelerators and beam transport lines is developed. The program is used for particle-in-cell simulation of axial-symmetric, quadrupole-symmetric and zuniform beams in a channel containing RF gaps, radio-frequency quadrupoles, multipole lenses, solenoids and bending magnets. The programming method includes hierarchical program design using program-independent modules and a flexible combination of modules to provide the most effective version of the structure for every specific case of simulation. Numerical techniques as well as the results of beam dynamics studies are presented.

Most planetary systems -including our own -are born within stellar clusters, where interactions with neighboring stars can help shape the system architecture. This paper develops an orbit-averaged formalism to characterize the cluster's mean-field effects as well as the physics of long-period stellar encounters. Our secular approach allows for an analytic description of the dynamical consequences of the cluster environment on its constituent planetary systems. We analyze special cases of the resulting Hamiltonian, corresponding to eccentricity evolution driven by planar encounters, as well as hyperbolic perturbations upon dissipative disks. We subsequently apply our results to the early evolution of our solar system, where the cluster's collective potential perturbs the solar system's plane, and stellar encounters act to increase the velocity dispersion of the Kuiper belt. Our results are two-fold: first, we find that cluster effects can alter the mean plane of the solar system by 1 deg, and are thus insufficient to explain the ψ ≈ 6 deg obliquity of the sun. Second, we delineate the extent to which stellar flybys excite the orbital dispersion of the cold classical Kuiper belt, and show that while stellar flybys may grow the cold belt's inclination by the observed amount, the resulting distribution is incompatible with the data. Correspondingly, our calculations place an upper limit on the product of the stellar number density and residence time of the sun in its birth cluster, η τ 2 × 10 4 Myr/pc 3 . Keywords: planets and satellites: dynamical evolution and stability, 4 ⇡ G c 2 ⇢/ c < l a t e x i t s h a 1 _ b a s e 6 4 = " F R + 8 I K r V C X 4 1 t B U A s y i g 5 M I Z k / w = " > A A A C F X i c b V D L S s N A F J 3 U V 6 2 v q E s 3 g 0 V w U W p S C r o s u t B l B f u A J o b J d N I O n W T C z E Q o I T / h x l 9 x 4 0 I R t 4 I 7 / 8 Z J m 4 W 2 H p j h c M 6 9 3 H u P H z M q l W V 9 G 6 W V 1 b X 1 j f J m Z W t 7 Z 3 f P 3 D / o S p 4 I T D q Y M y 7 6 P pr O 1 N 8 d K Q q l n I a + r s x 3 l 4 t e L v 7 n D R I V X L g p j e J E k Q j P B w U J g 4 r D P C I 4 p I J g x a a a I C y o 3 h X i M R I I K x 1 k R Y d g L 5 6 8 T L q N u m 3 V 7 d t m t X V Z x F E G R + A Y n A I b n I M W u A F t 0 A E Y P I J n 8 A r e j C f j x X g 3 P u a l J a P o O Q R / Y H z + A M r + n p 0 = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " F R + 8 I K r V C X 4 1 t B U A s y i g 5 M I Z k / w = " > A A A C F X i c b V D L S s N A F J 3 U V 6 2 v q E s 3 g 0 V w U W p S C r o s u t B l B f u A J o b J d N I O n W T C z E Q o I T / h x l 9 x 4 0 I R t 4 I 7 / 8 Z J m 4 W 2 H p j h c M 6 9 3 H u P H z M q l W V 9 G 6 W V 1 b X 1 j f J m Z W t 7 Z 3 f P 3 D / o S p 4 I T D q Y M y 7 6 P p K E 0 Y h 0 F F W M 9 G N B U O g z 0 v M n V 7 n f e y B C U h 7 d q W l M 3 B C N I h p Q j J S W P L P W d G p O T P U X I j X G i K X X m V P D 9 w 2 t i D E / c 9 q S e q k j w h R n m W d W r b o 1 A 1 w m d k G q o E D b M 7 + c I c d J S C K F G Z J y Y F u x c l M k F M W M Z B U n k S R G e I J G Z K B p h ...

An experiment (E166) at the Stanford Linear Accelerator Center (SLAC) has demonstrated a scheme in which a multi-GeV electron beam passed through a helical undulator to generate multiMeV, circularly polarized photons which were then converted in a thin target to produce positrons (and electrons) with longitudinal polarization above 80% at 6 MeV. The results are in agreement with Geant4 simulations that include the dominant polarization-dependent interactions of electrons, positrons and photons in matter.PACS . Polarized positrons can be produced via the pair-production process initiated by circularly polarized photons [2]. In a scheme proposed by Balakin and Mikhailichenko [3] a multi-GeV electron beam is passed through a helical undulator [4] to generate the needed multi-MeV photons with circular polarization. Alternatively, the circularly polarized photons can be produced by laser backscattering off an electron beam [5,6]. An experiment (E166) has been performed to demonstrate that the undulatorbased scheme can produce polarized positron beams of sufficient quality for use at the proposed International Linear Collider (ILC) [7]. The main elements of the experiment were the SLAC linac