# Alexander Henderson

## Contact Details

NameAlexander Henderson |
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## Pubs By Year |
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## Pub CategoriesMathematics - Classical Analysis and ODEs (2) High Energy Astrophysical Phenomena (2) Physics - Plasma Physics (2) Mathematics - Dynamical Systems (2) Physics - Accelerator Physics (2) Physics - Medical Physics (1) High Energy Physics - Experiment (1) Mathematics - Metric Geometry (1) Physics - Instrumentation and Detectors (1) |

## Publications Authored By Alexander Henderson

We show that self-similar sets arising from iterated function systems that satisfy the Moran open-set condition, a canonical class of fractal sets, are `equi-homogeneous'. This is a regularity property that, roughly speaking, means that at each fixed length-scale any two neighbourhoods of the set have covers of approximately equal cardinality. Self-similar sets are notable in that they are Ahlfors-David regular, which implies that their Assouad and box-counting dimensions coincide. Read More

It is known that, unlike the Hausdorff dimension, the Assouad dimension of a self-similar set can exceed the similarity dimension if there are overlaps in the construction. Our main result is the following precise dichotomy for self-similar sets in the line: either the \emph{weak separation property} is satisfied, in which case the Hausdorff and Assouad dimensions coincide; or the \emph{weak separation property} is not satisfied, in which case the Assouad dimension is maximal (equal to one). In the first case we prove that the self-similar set is Ahlfors regular, and in the second case we use the fact that if the \emph{weak separation property} is not satisfied, one can approximate the identity arbitrarily well in the group generated by the similarity mappings, and this allows us to build a \emph{weak tangent} that contains an interval. Read More

In a series of experiments at the Texas Petawatt Laser (TPW) in Austin, TX, we have used attenuation spectrometers, dosimeters, and a new Forward Compton Electron Spectrometer (FCES) to measure and characterize the angular distribution, fluence, and energy spectrum of the X-rays and gamma rays produced by the TPW striking multi-millimeter thick gold targets. Our results represent the first such measurements at laser intensities > 10 21 W*cm-2 and pulse durations < 150 fs. We obtain a maximum yield of X-ray and gamma ray energy with respect to laser energy of 4% and a mean yield of 2%. Read More

We present data for relativistic hot electron production by the Texas Petawatt Laser irradiating solid Au targets with thickness between 1 and 4 mm. The experiment was performed at the short focus target chamber TC1 in July 2011, with laser energies around 50 J. We measured hot electron spectra out to 50 MeV which show a narrow peak around 10 - 20 MeV plus high energy exponential tail. Read More

We report simulation results of pair production by ultra-intense lasers irradiating a gold target using the GEANT4 Monte-Carlo code. Certain experimental features of the positron and electron energy spectra are reproduced, as well as trends with regard to target thickness and hot electron temperature Te. For Te in the range 5-10 MeV, the optimal target thickness for pair production is found to be about 3 mm. Read More