58 research outputs found
Economical adjunction of square roots to groups
How large must an overgroup of a given group be in order to contain a square
root of any element of the initial group? We give an almost exact answer to
this question (the obtained estimate is at most twice worse than the best
possible) and state several related open questions.Comment: 5 pages. A Russian version of this paper is at
http://mech.math.msu.su/department/algebra/staff/klyachko/papers.htm V2:
minor correction
Experimental study of extended timescale dynamics of a plasma wakefield driven by a self-modulated proton bunch
Plasma wakefield dynamics over timescales up to 800 ps, approximately 100 plasma periods, are studied
experimentally at the Advanced Wakefield Experiment (AWAKE). The development of the longitudinal
wakefield amplitude driven by a self-modulated proton bunch is measured using the external injection of
witness electrons that sample the fields. In simulation, resonant excitation of the wakefield causes plasma
electron trajectory crossing, resulting in the development of a potential outside the plasma boundary as
electrons are transversely ejected. Trends consistent with the presence of this potential are experimentally
measured and their dependence on wakefield amplitude are studied via seed laser timing scans and electron
injection delay scan
Experimental study of wakefields driven by a self-modulating proton bunch in plasma
We study experimentally the longitudinal and transverse wakefields driven by a highly relativistic proton bunch during self-modulation in plasma. We show that the wakefields' growth and amplitude increase with increasing seed amplitude as well as with the proton bunch charge in the plasma. We study transverse wakefields using the maximum radius of the proton bunch distribution measured on a screen downstream from the plasma. We study longitudinal wakefields by externally injecting electrons and measuring their final energy. Measurements agree with trends predicted by theory and numerical simulations and validate our understanding of the development of self-modulation. Experiments were performed in the context of the Advanced Wakefield Experiment (AWAKE)
Transition between Instability and Seeded Self-Modulation of a Relativistic Particle Bunch in Plasma
We use a relativistic ionization front to provide various initial transverse wakefield amplitudes for the self-modulation of a long proton bunch in plasma. We show experimentally that, with sufticient initial amplitude [>= (4.1 +/- 0.4) MV/m], the phase of the modulation along the bunch is reproducible from event to event, with 3%-7% (of 2 pi) rms variations all along the bunch. The phase is not reproducible for lower initial amplitudes. We observe the transition between these two regimes. Phase reproducibility is essential for deterministic external injection of particles to be accelerated
Proton Bunch Self-Modulation in Plasma with Density Gradient
We study experimentally the effect of linear plasma density gradients on the self-modulation of a 400 GeV proton bunch. Results show that a positive or negative gradient increases or decreases the number of microbunches and the relative charge per microbunch observed after 10 m of plasma. The measured modulation frequency also increases or decreases. With the largest positive gradient we observe two frequencies in the modulation power spectrum. Results are consistent with changes in wakefields' phase velocity due to plasma density gradients adding to the slow wakefields' phase velocity during self-modulation growth predicted by linear theory
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