OSCILLATIONS IN A SYNCHROTRON UNDER SPACE CHARGE CONDITIONS
OSCILLATIONS IN A SYNCHROTRON UNDER SPACE CHARGE CONDITIONS
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空间电荷条件下同步加速器的振荡
DOI：
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发表时间：
1964
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影响因子：
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通讯作者：
P. Lapostolle
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作者：
P. Lapostolle
空间电荷是加速器的一个基本限制，也是决定目前传统同步加速器强度的实际过程。对于正在取代传统高能同步加速器的AG或强聚焦同步加速器，也必须有类似的空间电荷限制，尽管还没有经历过。为了设计新的机器，已经计算出一个公式，该公式是基于由于空间电荷力引起的电子感应加速器频率的变化和v数不应穿过任何整数或半整数共振的条件[1]。事实上，正如Morin [2]所指出的，由于空间电荷力与电子束的位置有关，并且不影响电子束的中心，所以在修正的v整数上不发生由场误差引起的共振，因此，无论空间电荷是大的还是可以忽略的，场误差共振总是发生在同一个地方。相反，梯度误差共振对修改外部聚焦力的空间电荷敏感。但是从欧洲核子研究中心和布鲁克海文的实验中可以知道，这种共振并不像另一种共振那样危险，而且有可能跨越它。我们打算在这里展示一种效应，它甚至可能有助于跨越这些共振，并使AG同步加速器中真正的空间电荷极限大大消除。空间电荷力取决于电子束的横向尺寸。如果注入同步加速器的光束与聚焦图案相匹配，则其横向尺寸几乎恒定（忽略AG聚焦的蠕动因子），并且空间电荷力也几乎恒定。但是如果不匹配，或者由于共振，会引起较大的振荡，则同步加速器中的束流包络会出现斜坡扇形。在这种情况下，聚焦力沿轨道沿着变化，甚至可以交替变化。产生了某种周期性聚焦。最终结果是整体聚焦效应的增加，这减小了电子感应加速器波长，并且倾向于在没有空间电荷的情况下将v恢复到其值v0。这种现象显然有助于消除用完全匹配束计算的空间电荷极限。
Space charge is a fundamental limitation in accelerators and is in practice the process which determines the intensity in present con ventional synchrotrons. For AG or strong fo cusing synchrotrons which are taking place of conventional ones for high energies, there must also be a similar space charge limitation, though it has not yet been experienced. For the design of new machines a formula has been computed which is based on the change in betatron frequency due to space charge forces and the condition that the v number should not cross any integral or half integral reso nance [1]. In fact, as shown by Morin [2], resonances induced by field errors do not occur on the modified v integers, since space charge forces are dependent of beam position and do not affect the middle of it. So that field error resonan ces always occur in the same place whether space charge is large or negligible. Gradient error resonances on the contrary are sensitive to space charge which modifies the external focusing forces. But one knows from the expe rience in CERN and Brookhaven that this type of resonance is not so dangerous as the other one and that it is possible to cross it. We intend to show here an effect which might even help in crossing these resonances and remove very far the true space charge limit in AG synchrotrons. Space charge forces depend on the transverse dimensions of the beam. If the beam injected into the synchrotron is matched to the focusing pattern, its transverse dimensions are nearly constant (neglecting the wriggling factor of the AG focusing) and space charge forces are also nearly constant. But if it is not matched or if, due to a resonance, larger oscillations are induced the beam enve lope scallopes in the synchrotron. In this case focusing forces vary along the orbit and can even alternate. Some kind of periodic focu sing is produced. The net result is an increase in overall focusing effect, which reduces the betatron wavelength and tends to restore v in its value v0 without space charge. Such a phenomenon is obviously to help removing space charge limit as computed with a per fectly matched beam.