Electro-magnetic

2.2.1 Beam Current Transformers

A beam current transformer (BCT) consists of a toroid of magnetic material placed around a non-conducting ceramic section of the beam pipe. This toroid couples to the magnetic field of the beam, which then acts as the primary of the transformer. A secondary winding is applied evenly around the toroid, and the current induced in this wire can be considered directly proportional to the beam current [46]. The ceramic gap prevents the image current from

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passing through the BCT aperture and cancelling the magnetic field of the beam. An alternative path is arranged to allow the image current to pass outside the BCT.

This method is not sensitive to the DC component of the beam current. Such a transformer is therefore useful only with bunched beams. If the secondary coil is read out using a suitably fast Analogue to Digital Converter (ADC), the currents of individual bunches can be distinguished and this is known as a fast beam current transformer (FBCT). However, the time resolution is still limited by the impedance of the coils and reaches at best a few tens of ns [47], making it unsuitable for the measurement of ghost and satellite bunches in the LHC, which have a spacing of 2.5 ns.

The BCT principle can be adapted to measure DC current [48]. In this case, two toroids are needed, each with two separate sets of secondary windings. One set of these windings is attached to the output amplifier. The other is excited by a sine wave modulation with amplitude sufficient to drive the magnetic toroid into saturation at the peaks of the wave. The excitation windings of the two toroids are connected in series so that the current they carry is exactly the same, but are wound in opposite directions. The output windings are also connected in series, so that the resulting current from the two toroids, being excited in opposite directions, is zero. If, however, an additional current, the beam, passes through the toroids, one of the two will saturate for a longer period than the other, and this asymmetry will result in a current being induced in the output windings. This system is known as the DC current transformer (DCCT or DC-BCT).

In order to improve the linearity and dynamic range of the DCCT, it is usually operated as a zero-flux current transformer. A wire passes through the aperture of both toroids and carries a compensation current which cancels the effect of the beam. This compensation current is automatically adjusted so that no current is measured on the output windings, the size of the compensation current is then a direct measure of the beam current (Figure 9). A DCCT in this configuration is often the only instrument which allows direct current measurement, and is then used to calibrate the FBCT and all other current-measurement instruments. The current sensitivity is typically 1-2 µA, equivalent to one tenth of a pilot bunch in the LHC [48]. When a larger current is circulating the accuracy of the current measurement can be as low as 0.2% [49].

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Figure 9. Schematic of a DC Current Transformer operating in zero-flux mode. From [50].

2.2.2 Wall Current Monitor

As the beam passes through the beam pipe, its electric field drags an equal but opposite ‘image current’ along the beam pipe. Wall Current Monitors (WCM) also use a non-conducting ceramic gap in the beam pipe to force this image current to find a new path. This is provided by a set of identical resistors evenly spaced around the gap. The voltage across these resistors is summed, in order to avoid a dependence on beam position, and is measured by a fast sampling oscilloscope [51]. The WCM can measure the beam current with a bandwidth of kHz to a few GHz. It can therefore be used for longitudinal profile measurement as well as bunch-by-bunch current measurement.

2.2.3 Electro-optic

Electro-optic (EO) techniques have been used to measure ultra-short electron bunches such as those used in FELs [52]. Time resolutions of a few tens of femtoseconds have been achieved [53]. The method uses a non-linear crystal such as gallium phosphide, which has the property of rotating the polarisation of light passing through it by an amount which is proportional to the electric field in the crystal. The crystal is placed inside the beam pipe where it sees the electric field of the beam. Crossed polarisers are fixed either side of the crystal, so that in the absence of any EO effect no light is transmitted. When an electric field is applied, however, the polarisation of the light is rotated between the two polarisers and some light is transmitted.

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The intensity profile of light transmitted through the crystal is therefore the same as the bunch profile.

A spectral encoding technique is usually used to measure the intensity profile of the light with sufficiently high temporal resolution. A laser pulse is generated with a wavelength chirp, that is, with wavelength changing with time through the pulse. The laser can be located outside the beam pipe, and the pulse is passed through the crystal using thin windows and mirrors. The pulse is synchronised to pass through the crystal at the same time as the bunch. Because of the wavelength chirp, the bunch profile is then encoded in the spectrum of the light as well as in its time profile. A spectrometer is used to read out the profile.