Relativistic Charged Beam Interactions

大型强子对撞机（LHC）计划于2006- 2007年投入运行，旨在探索质子能量超过100亿电子伏特的中心碰撞中产生的多夸克相互作用。它可能会发现包括标量场在内的新粒子存在的证据。然而，即使发展到更高的能量，它也不可能解决基本相互作用的标准模型所提出的所有悬而未决的问题。它的碰撞成分（质子）是复合的，因此束能量在单个夸克之间分配。另一种方法是使用直接加速轻子和反轻子点状结构的装置。事实上，这样的机器有着经过良好测试的血统。大多数标准模型的详细精度测试归功于欧洲核子研究中心（日内瓦）的电子-正电子环对撞机（LEP）。新一代电子/正电子线性对撞机目前正在SLAC（美国）、DESY（德国）、KEK（日本）的ILC和欧洲核子研究中心（CLIC）的设计过程中，投射能量在1 Tev区域。无论大型强子对撞机或这些新的电子/正电子对撞机的结果如何，超越标准模式的全面预测无疑需要几台TeV的电子-正电子机器，才能在产生的数据中出现明确的模式。将电子/正电子机器缩放到更高的能量只能在线性对撞机上实现。欧洲核子研究中心开发了一种全新的高能电子/正电子线性对撞机（linac）。紧凑型直线对撞机（CLIC）因其与其他设计相比横向尺寸紧凑而得名。这种复杂装置的有效运行依赖于当前技术可行性极限的许多挑战。为了达到设计标准，需要对光束的相干同步辐射的作用有更充分的了解，其有效的功能依赖于能够控制这种发射。到目前为止，这个问题仍有待完全解决。描述带电物质在电磁场下的相对论性行为的封闭偏微分方程组的数学上连贯的公式不可避免地是非线性的，并且在一般情况下满足因果边界条件的精确解是难以解决的。在许多新提出的先进设备中，（相干和非相干）辐射对微尺寸带电束的影响是发展的一个重大障碍，这表明用于模拟这种效应的现有方法是不充分的，重新审视整个问题是及时的。这一建议的目的是提供新的工具，在微分几何分析一个新的近似方案基本上基于光锥结构的时空。它旨在与英国，欧洲核子研究中心，DESY和美国的加速器科学家在18个月的时间内进行互动，以确定在设计新颖和先进设计的拟议设备时与同步辐射相关的问题的确切性质。根据与主要加速器中心人员的互动，计划用一个新的理论方案来面对上述问题，这将导致对经典和量子同步辐射现象的更清晰的理解，并为解决这些问题提供新的工具。特别是，它将允许构建新的高效和透明的代码，以应对与上述提议机器（CLIC）中阻尼和组合环的计划功能相关的挑战，并为数学科学提供新的电动力学框架。

The Large Hadron Collider (LHC) scheduled for operation in 2006-7is planned to explore multi-quark interactions that arise incentral collisions with a proton energy of over a million million electron volts.It may uncover evidence for new particles including scalar fields.However even if developed to higher energies it is unlikely toresolve all the outstanding questions raised by the standard modelof the fundamental interactions. Its colliding constituents(protons) are composites and therefore the beam energy ispartitioned among individual quarks. An alternative is to use adevice that accelerates directly the point-like structure ofleptons and anti-leptons. Indeed such a machine has a well testedpedigree. Most of the detailed precision tests of the standardmodel owe their success to the electron-positron ring collider(LEP) at CERN (Geneva), A new generation of electron/positronlinear colliders is now in design progress at SLAC (USA), DESY(Germany), KEK (Japan) for the ILC and at CERN for CLIC withprojected energies in the 1 Tev region. Whatever the outcome ofthe LHC or these new electron/positron colliders, the fullpanoply of predictions beyond the standard mode will undoubtedlyrequire several TeV electron-positron machines before definitivepatterns can emerge in the data produced.Scaling electron/positron machines to higher energies can onlybe realistically achieved for LINEAR colliders. A radically newdesign for a higher energy electron/positron linear collider(linac) has been developed at CERN. The Compact Linear Collider(CLIC) gains its name from its compact transverse dimensioncompared with other designs. The effective operation of such acomplex device relies on a number of challenges that lie at thelimit of current technological feasibility. The role of coherentsynchrotron radiation by the beam requires a fuller understandingin order to achieve design criteria and its effective functioning relies on being able to control such emission. To date this problem remain to be fully resolved.A mathematically coherent formulation of a closed system ofpartial differential equations describing the relativisticbehaviour of charged matter with electromagnetic fields isinevitably non-linear and in general exact solutions satisfyingcausal boundary conditions are intractable. The fact that theeffects of (coherent and incoherent) radiation on micro-sizedcharged bunches in a host of newly proposed advanced devices is asignificant barrier to development indicates that existingapproaches used to model such effects are inadequate and that afresh look at the whole problem is timely. It is the aim of thisproposal to offer new tools in differential geometry to theanalysis of a new approximation scheme based fundamentally on thelight cone structure of spacetime.It is aimed to interact with accelerator scientists in the UK,CERN, DESY and the US, over a period of 18 months, to determine the precise nature of theproblems associated with synchrotron radiation in the design ofproposed devices of novel and advanced design. Based oninteractions with personnel in major accelerator centres it isplanned to confront the above problems with a new theoreticalprogramme that will lead to a clearer understanding of classicaland quantum synchrotron radiation phenomena and provide new toolsfor their solution. In particular it will permit the constructionof new efficient and transparent code for tackling the challengesassociated with the planned functioning of the damping andcombiner rings in the proposed machine (CLIC) described brieflyabove and provide a new electrodynamics framework for themathematical sciences .