TU CE GSC CE People at the Graduate School CE Alumni Mouhammad Alhumaidi Research Project of Mouhammad Alhumaidi

Methods from statistical signal processing for application in accelerator technology

Particle accelerators are very important facilities for fundamental and applied research in physics. The basic idea of these facilities is to accelerate charged particles, e.g. heavy ions at the GSI, using electromagnetic fields. Based on the path particles take during acceleration, there are two main types of particle accelerators:

- Linear Accelerators (Linac): where particles are accelerated in a straight line. They usually provide the required energy for the injection into circular accelerators.
- Circular or Cyclic Accelerators: where particles are accelerated in a circule, until they reach the desired energy, where they will be extracted for experiments. The advantage of this kind of accelerators over Linacs is that the particles can travel very long distances during acceleration to nearly reach the speed of light. Therefore, they can have much higher energy. Synchrotron is an example of circular accelerators.

Our project is concerned with the heavy ions sychrotron SIS 18 at the GSI Helmholzzentrum.

To keep the particles at the wanted trajectory inside the vacuum tube, deflecting and focusing forces have to be applied on them. This is guaranteed by means of the different types of electromagnets, e.g. quadrupoles, sextupoles, ... etc. see Figures 1 and 2.

During the acceleration instabilities can emerge due to the interaction between the beams and the different accelerator parts. This can lead to beam loss. In our project we address coherent coupled-bunch instabilities.

The demand for higher beam intensities is always increasing in particle accelerators. The wake fields generated by the traveling particles will be increased by increasing beam intensity. Therefore, the interaction between beams and the different objects of the accelerator will also be increased. This will lead to increasing instabilities. These instabilities can be either transversal or longitudinal. In our project we are interested in transversal instabilities.

This kind of instabilities is called coupled-bunch instabilities, since they are generated by coherent interaction between bunches and the accelerator objects.

There are many sources of coupled-bunch coherent instabilities like:

- High Order Modes of Cavities: The beam can excite higher order resonance frequencies of the accelerating cavities, which will excite beam instabilities.
- Resistive Wall Impedance: Generated by the interaction between the beam and the vacuum tube due to its finite conductivity.
- Space Charge Impedance: Generated by the capacitive coupling between the beam and the vacuum tube.
- ... etc.

The different parts of the accelerator should be optimized to increase the natural damping, which decrease instabilities. However usually for higher beam intensities, the natural damping alone is not able to prevent instabilities. Therefore the use of active measures against instabilities is mandatory, in order to stabilize the beam.

Feedback systems sense instabilities of the beam by means of Beam Position Monitors (BPM), and acts back on the beam by means of actuator called Kicker, such that the beam will be stabilized.

The signal of BPM represents the distance of the beam from the ideal trajectory at a certain position of the BPM. The signals of many BPMs at different positions will be digitized to be processed digitally, in order to determine the driving signal at the kicker. This signal will be converted into the analog domain and amplified to drive the kicker. The kicker deflects the beam proportionally to the input signal. Our project is concerned with stabilizing transversal instabilities. See Figure 3.

A New concept for using multiple pickups for estimating beam angle at the kicker has been addressed. The estimated signal should be the driving feedback signal. The signals from the different pickups are delayed, such that they correspond to the same bunch. Consequently a weighted sum of the delayed signals is suggested as an estimator of the beam angle at the kicker. The weighting coefficients are calculated such that the estimator is unbiased, i.e., the output corresponds to the actual beam angle at the kicker for non-noisy pickup signals. Furthermore, the estimator must give the minimal noise power at the output among all linear unbiased estimators. Finally results for the heavy ions synchrotron SIS 18 at the GSI are shown.

In the SIS 18 there are 12 beam position pickups, which are located periodically along the synchrotron ring. There is also one transversal feedback kicker. The phase differnce between each two neighbour pickups corresponds to the machine tune divided by 12, which is 129.3◦ for the horizontal dircection and 99.2◦ for the vertical dircection. During the acceleration The focusing changes continuously from triplet mode to doublet mode. Since we have two transversal directions, i.e. horizontal x and vertical y, we will show simulation results for four different scenarios. The results are depicted in Figures 1-4. As a reference we take the noise power for using the closest two pickups to the kicker. For each scenario two curves are depicted, i.e. the noise power for using increasing number of the closest pickups to the kicker and the noise power for using the best combinations of increasing number of pickups. The figures show, that the noise power can be reduced by about 6.5 db for x-direction and about 3.5 db for y-direction just by using the best two pickups combination rather than the closest two pickups to the kicker.

Multi-Physics; Particle Accelerator: Statistical Signal Processing

Mouhammad Alhumaidi

M.Sc.

Address: | Dolivostraße 15 |

D-64293 Darmstadt | |

Germany | |

Phone: | +49 6151 16 - 24401 or 24402 |

Fax: | +49 6151 16 - + 49 6151-16 3778 |

Office: | S3 / 06 / |

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