Kirchhoff ’ s Integral Representation and a Cavity Wake Potential ∗
نویسنده
چکیده
A method is proposed for the calculation of the short-range wake field potentials of an ultra-relativistic bunch passing near some irregularities in a beam pipe. The method is based on the space-time domain integration of Maxwell’s equations using Kirchhoff’s formulation. We demonstrate this method on two cases where we obtain the wake potentials for the energy loss of a bunch traversing an iris-collimator in a beam pipe and for a cavity. Likewise, formulas are derived for Green’s functions that describe the transverse force action of wake fields. Simple formulas for the total energy loss of a bunch with a Gaussian charge density distribution are derived as well. The derived estimates are compared with computer results and predictions of other models.
منابع مشابه
Line integrals and physical optics . Part II . The conversion ita of the Kirchhoff surface integral to a line integral
A new approach is presented for converting the surface integral, representing the Kirchhoff diffracted field of an aperture on a plane screen, to a line integral. It has the advantages that it is mathematically rigorous and explicit and that it results in a representation that has exactly the same properties as the original Kirchhoff formula, i.e., it admits arbitrary source distributions and i...
متن کاملFinite groups admitting a connected cubic integral bi-Cayley graph
A graph is called integral if all eigenvalues of its adjacency matrix are integers. Given a subset $S$ of a finite group $G$, the bi-Cayley graph $BCay(G,S)$ is a graph with vertex set $Gtimes{1,2}$ and edge set ${{(x,1),(sx,2)}mid sin S, xin G}$. In this paper, we classify all finite groups admitting a connected cubic integral bi-Cayley graph.
متن کاملClassical free-streamline flow over a polygonal obstacle
In classical Kirchhoff flow, an ideal incompressible fluid flows past an obstacle and around a motionless wake bounded by free streamlines. Since 1869 it has been known that in principle, the two-dimensional Kirchhoff flow over a polygonal obstacle can be determined by constructing a conformal map onto a polygon in the log-hodograph plane. In practice, however, this idea has rarely been put to ...
متن کاملA representation for some groups, a geometric approach
In the present paper, we are going to use geometric and topological concepts, entities and properties of the integral curves of linear vector fields, and the theory of differential equations, to establish a representation for some groups on $R^{n} (ngeq 1)$. Among other things, we investigate the surjectivity and faithfulness of the representation. At the end, we give some app...
متن کاملA remark on asymptotic enumeration of highest weights in tensor powers of a representation
We consider the semigroup $S$ of highest weights appearing in tensor powers $V^{otimes k}$ of a finite dimensional representation $V$ of a connected reductive group. We describe the cone generated by $S$ as the cone over the weight polytope of $V$ intersected with the positive Weyl chamber. From this we get a description for the asymptotic of the number of highest weights appearing in $V^{otime...
متن کامل