Bibliography

Footnotes

¹ Although the top quark was discovered after the bottom, it was one of the most widely predicted particles ever to be discovered. In fact, one could say that the last truly unexpected new particle to be discovered was the charm quark, since the discovery of the J/ψ in 1974 allowed confirmation of the quark model and precipitated the “November Revolution”; the bottom quark was merely considered an extension to the quark/parton model, already proposed as part of the CKM mechanism of quark mixing and prompted by the discovery of the tau lepton in 1975 [1].

² Gravity has proved to be the one stumbling block that the Standard Model has been unable to account for. It is one of the aims of “Quantum Gravity” theories to be able to unify the Standard Model forces with General Relativity to place all the known forces of nature on an equal footing. The preliminary suggestion is that gravity is mediated by a spin-2 boson called the graviton.

³ It has been said that “The predictions of the Higgs sector and supersymmetry are likely to be completely wrong, but are our only useful reference point.” [3]

⁴ Neutrino oscillations arise from a mixing of the mass eigenstates with respect to the weak neutrino eigenstates: this essentially means that, while retaining their weak eigenstate, neutrinos can oscillate between the mass eigenstates. This is similar to the mixing of quarks that results in flavour-changing quark decays, mediated by the W^±, and is only possible if the neutrinos have mass.

⁵ Conseil Européen pour la Recherche Nucléaire, or European Organisation for Nuclear Research.

⁶ It is theoretically possible to set the initial spin states of both leptons in an e⁺e⁻ collision: experimentally, certain difficulties must be overcome, such as the production of spin-polarised positrons, that reduce the net spin polarisation of the two beams to less than 100%.

⁷ The current design for the NLC includes an option for two IP's — one high and one low energy (see Fig. 1.3) — but the two cannot be operated concurrently, since each bunch can only be used once.

⁸ The energy loss from synchrotron radiation is actually dependent on γ⁴, where γ² = 1/(1 − v² / c²) for a particle with velocity v. Since γ = E/m₀c², for a particle of rest mass m₀, this gives the E⁴ and 1/m⁴ dependence of the synchrotron energy loss [15].

⁹ This process is more economical for circular accelerators, since each bunch can be recycled rather than being accelerated from scratch.

¹⁰ A number of different layouts exist for the NLC, dependent primarily upon its location. The near-surface cut-and-cover configuration is designed for use in the suggested site in the Great Central Valley in California, with the deep-bored-tunnel design intended for use at the Fermilab site in Northern Illinois [13].

¹¹ At the SLC the beam was modelled as a Gaussian distribution of particles, with a 1% tail that extends essentially to infinity (the ‘halo’). The beam dimensions — σ_x and σ_y — are therefore equivalent to the r.m.s. width of this Gaussian. This beam model profile is assumed here.

¹² Since the angle of a particle trajectory, in a particular plane (say x), also defines the rate of change of position within that plane, the angle is denoted by the symbol for velocity (x′).

¹³ Wigglers are also used in synchrotron light sources, due to the narrow spread of very high intensity synchrotron radiation that they produce.

¹⁴ A radiation length, χ₀, is defined as the depth of material required to reduce the energy of an incident particle to 1/e of its initial value, and is unique to each material.

¹⁵ All magnets behave in this fashion, acting like the next-lowest-order magnet whose strength varies with distance from the magnet centre i.e. a quadrupole acts like a dipole with a bending radius that is a function of horizontal position and a sextupole acts like a quadrupole with a focal length that is a function of horizontal position.

¹⁶ For the simpler rectangular waveguides only 2 subscripts (mn) are required and are related to the height and width of the waveguide cross section. For more complex cylindrical waveguides, such as an accelerating cavity, three subscripts are used: TM_mnl, which indicate the azimuthal, radial and longitudinal mode numbers respectively. The azimuthal mode number is zero for azimuthally symmetric modes; the radial mode number minus one is the number of nodes in the radial variation of the E-field; the longitudinal mode number is zero for a constant longitudinal E-field [39].

¹⁷ The inner (or iris) diameter of the disks can actually vary along the length of the structure, depending on whether the structure is a constant gradient or constant impedance structure [38].

¹⁸ Initial State Radiation, or ISR, is the emission of a photon by one of the two initial state particles prior to collision. This is a stochastic process and results in a spread in the collision energy of the beam.

¹⁹ The latency of the system is defined as the combined flight time of the incoming beam to the kicker and the outgoing beam to the BPM, plus the signal propagation delay through the IPFB electronics. In other words, the time it takes for the BPM to measure an offset, pass a signal to the kicker, have the kicker correct the beam and finally see the results of this correction. This is predicted to be on the order of 30 ns for the real system: 2×12 ns time-of-flight from IP to the IPFB system (situated ~4 m from the IP), plus 6 ns processing time [58].

²⁰ Baseband is the frequency space enthusiast's term for a signal that tends towards DC, or a signal with a dominant component at zero Hertz.

²¹ Other such active filters include the Chebyshev (fast rolloff from passband to stopband) and Butterworth (maximum flatness of frequency within the passband) [62].

²² When driven as a modulator i.e. when upconverting a signal to a high frequency and making use of the ω₁ + ω₂ frequency, the input signal to be modulated is normally input into the IF port, with the resulting high frequency signal coming from the RF port; the LO remains unchanged.

²³ Other mixer types include single-balanced — consisting of a pair of diodes — and single-ended, with just a single diode. As the mixer layout increases in complexity, there is a corresponding improvement in port isolation and reduction in intermodulation products [63].

²⁴ An IP-BPM flight time of 6.6 ns corresponds to the IPFB system being ~2 m downstream of the IP. This is unlikely to be the true location, since it places the IPFB system well within the detector; however, it does not affect the principle of operation of the system.

²⁵ Appropriately-modified in this context means that the filter frequencies would have to be correctly tuned for the E158 bunch spacing i.e. 2856 MHz. The LO input for the mixer would therefore also be set to 2856 MHz.

²⁶ The klystron gallery is the building that sits directly above the accelerator tunnel, above ground, and houses the klystrons that power the linac accelerating structures.

²⁷ © Glen White, 2001.

²⁸ The given beam energy is for an unaccelerated beam, in which only the pre-accelerator that resides upstream of the chicane is used to power the beam, rather than any of the test structures downstream of the chicane.

²⁹ 100 µm / 10 µm vertical jitter = a factor of 10; 62 MeV / 1.2 GeV = a factor of 1/20^th. Therefore the beam has to be kicked 10/20 = 1/2 as far for the NLCTA as for Sector 2.

³⁰ For example, in the SLC, the BPM processors used for the stripline BPM's, with ~10 cm strips (giving F_c ≈ 714 MHz), filter the signal at 30 MHz. This is significantly cheaper than filtering at 714 MHz, and given the large number of BPM's involved is the most cost-effective solution [83].

³¹ Kimball Physics part no. for spherical cube: MCF133-SC6-A.

³² BPM assembly and pickoff tuning procedure carried out by Gavin Nesom, Oxford University.

³³ 0 dBm = 1 mW. The relation between dBm and mW is: mW = 10^(dBm/₁₀) or 10log₁₀(mW) = dBm.

³⁴ Although the Gunn diode is not a diode in the strict sense, since the I-V behaviour is the same for both positive and negative applied voltage, it is this nonlinear behaviour, between V_peak and V_valley, that gives it its name.

³⁵ Strictly speaking power can pass in both directions through an isolator, but the attenuation in the backwards direction is some four orders of magnitude higher than the forward direction: the measured attenuation for the isolators used was 1.3 dB for the forward direction and 41 dB for the backward. This enormous difference in signal attenuation gives the isolator its directional behaviour.

³⁶ Power reduction factor = 10^dB/₁₀; voltage reduction is the square root of this value since P ∝ V².

³⁷ The definition of σ for the two pulse types is different: the Gaussian pulse uses the usual definition, with ~63% of the particles in the bunch contained within ±1σ; for the square pulse, σ is half the pulse width.

³⁸ The 15 dB attenuator was used as the original 10 dB attenuator could not be located at the time the measurement was made. It is possible that the S₁₁ loss for the 10 dB attenuator is smaller than that measured for the 15 dB attenuator, giving a value for the total attenuation closer to the measured reflection.

³⁹ The 2-way Splitter/Combiners used were Pulsar Microwave 2-way stripline power dividers, part no.: PS2-16-450/8S [101].

⁴⁰ The mixer output becomes nonlinear with an RF input greater than +5 dBm, as can be seen in Fig. 4.23.

⁴¹ All the phase shifters used were MCE/Weinschel coaxial phase shifters; model no.: 980-4 [102].

⁴² The isolators used were Nova Microwave connectorized SMA isolators, model no.: 1070IES [103].

⁴³ The 4-way Splitter/Combiner used was a Pulsar Microwave 4-way stripline power divider, part no.: PS4-12-452/7S [105].

⁴⁴ One of this pair of phase shifters is essentially redundant, since only one is required to adjust the relative phase between the two signal paths. However, since both the phase and signal attenuation of both paths had to be exactly matched, it is much simpler to achieve this with a pair of identical phase shifters.

⁴⁵ Due to the multiplication process of the mixer, two completely in phase signals of identical frequency produce a maximally positive output; for a 180° phase difference the output is maximally negative. A phase difference of ±90° between the two signals produces no output.

⁴⁶ The signal was made maximally negative, rather than positive, since the BPM was required to produce a negative output if the beam was low of centre, and a positive output if the beam was high of centre.

⁴⁷ It is possible that the stripline BPM response may become nonlinear for a beam that is a significant fraction of the beampipe diameter away from the centre [30,61]. A dipole magnet, however, should show no such nonlinearity, so the fact that such a clear linear response is evident in Fig. 4.38 is an excellent indication that the position as measured by the BPM is correct.

⁴⁸ Roughly speaking, a 10% signal difference of this nature corresponds to a 10% larger signal pickup on one pickoff with respect to the other i.e. the beam is closer to one pickoff by 10% of the pickoff spacing. For a cavity size of 35 mm, this corresponds to a beam off-centre by 1.67 mm, not an unreasonable figure given the range shown in Fig. 4.38.

⁴⁹ At least, if there are problems with the BPM processor that are causing the appearance of these artefacts in the normalised position measurement, they are certainly repeatable.

⁵⁰ A number of attempts were made to produce a complete 2-D profile scan of the aperture of the beampipe of the FONT BPM using the integrated charge measured by the toroid and the BPM sum signal. However, due to the rapid deterioration of the beam, even over the course of a couple of minutes, coupled with the length of time required to record the position measurements and change the magnet currents, it proved impossible to do so.

⁵¹ The error is calculated from the mean r.m.s. spread of the position measurements shown in Fig. 4.59.

⁵² Magnets identified and located by Cherrill Spencer and released by Jim Allen.

⁵³ Data on NLCTA dipole and quadrupole magnet gradients taken from the SCP.

⁵⁴ It is therefore likely, since the shape of the curves in Figs. 4.57 and 5.14 for both the sum signal and toroid is so similar, that the signal degradation is a result of the aperture of the FONT BPM. Since the transmission profile of all the measurements shows no plateau, the likelihood is that the beam is larger than the FONT BPM beampipe diameter.

⁵⁵ Magnets identified and located by Paul Stephens and Marc Ross and released by Jim Allen.

⁵⁶ The designation of pairs of connectors as ‘input’ and ‘output’ is essentially redundant, and dependent only on the pair to which the supply voltage is connected: there is no mechanical or electrical difference between any of the four connectors. In practice, only one input and output connector is used: the kicker assembly has four connectors, rather than two, to allow the connection of a second power supply to allow a greater voltage to be applied.

⁵⁷ 1 T = 10⁴ G ⇒ 1 T-m = 10 kG-m.

⁵⁸ Q-switch power supply, ID 102-002, designed, built and supplied for FONT's use by Dave Brown at SLAC.

⁵⁹ A Pockels cell is a high speed optical switch that uses a voltage to modulate the refractive index of a crystal. A fast, high voltage power supply is required to change the field applied to the crystal at high speed, allowing fast switching of an optical source, such as a laser.

⁶⁰ A gain of 5 rather than 4 is used for the output amplifier to take account of the inherent gain of each of the multiplier chips of 0.95, as well as any transmission loss.

⁶¹ DC supply board machined and assembled by Matt Sorgenfrei at SLAC.

⁶² NLCTA control and DAQ is split between two micro's: TA01, primarily responsible for the front half of the accelerator, up to quad QD1110, and TA02, used for the rear section of the accelerator.

⁶³ In truth, the Z offset adjust is not necessary, since the feedback circuit itself removes any DC offset through its AC-coupled inputs (see Fig. 5.24). However, the addition of such adjusts was neither time consuming nor detrimental to the operation of the circuit, so they were included in the same fashion as before.

⁶⁴ Beam length measurements taken from the SCP.

⁶⁵ The net offset merely means that the beam is displaced slightly further downwards than if the FONT dipole were operating alone. Since the kicker and dipole magnets occupy the same location, the net effect is as if the dipole had been steered slightly downwards. Any such offset can therefore be taken out with the dipole.

⁶⁶ To prevent the AWG 1/Q signal overdriving the input of the normaliser stage, the AWG output is limited to 2 V. This means that, at the start of the beam pulse, when the beam charge is low, the AWG pulse is artifically low. This limits the usable pulse length to that with a large enough beam charge, and results in approximately the first 5 ns of the pulse being unusable. The same is also true for the end of the pulse.

⁶⁷ A 14 dB attenuator provides a factor of 25 reduction in power and therefore a factor 5 reduction in voltage, dropping the peak-to-peak voltage to the BPM sum input to 200 mV.

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© Simon Jolly 2003