Weighted Radon transforms for which the Chang approximate inversion formula is precise

We describe all weighted Radon transforms on the plane for which the Chang approximate inversion formula is precise. Some subsequent results, including the Cormack type inversion for these transforms, are also given

First operation and performance of a 200 lt double phase LAr LEM-TPC with a 40x76 cm^2 readout

In this paper we describe the design, construction, and operation of a first large area double-phase liquid argon Large Electron Multiplier Time Projection Chamber (LAr LEM-TPC). The detector has a maximum drift length of 60 cm and the readout consists of a $40\times 76$ cm$^2$ LEM and 2D projective anode to multiply and collect drifting charges. Scintillation light is detected by means of cryogenic PMTs positioned below the cathode. To record both charge and light signals, we have developed a compact acquisition system, which is scalable up to ton-scale detectors with thousands of charge readout channels. The acquisition system, as well as the design and the performance of custom-made charge sensitive preamplifiers, are described. The complete experimental setup has been operated for a first time during a period of four weeks at CERN in the cryostat of the ArDM experiment, which was equipped with liquid and gas argon purification systems. The detector, exposed to cosmic rays, recorded events with a single-channel signal-to-noise ratio in excess of 30 for minimum ionising particles. Cosmic muon tracks and their $\delta$-rays were used to assess the performance of the detector, and to estimate the liquid argon purity and the gain at different amplification fields.Comment: 23 pages, 21 figure

Test of a Liquid Argon TPC in a magnetic field and investigation of high temperature superconductors in liquid argon and nitrogen

Tests with cosmic ray muons of a small liquid argon time projection chamber (LAr TPC) in a magnetic field of 0.55 T are described. No effect of the magnetic field on the imaging properties were observed. In view of a future large, magnetized LAr TPC, we investigated the possibility to operate a high temperature superconducting (HTS) solenoid directly in the LAr of the detector. The critical current $I_c$ of HTS cables in an external magnetic field was measured at liquid nitrogen and liquid argon temperatures and a small prototype HTS solenoid was built and tested.Comment: 5 pages, 5 figures, to appear in Proc. of 1st International Workshop towards the Giant Liquid Argon Charge Imaging Experiment (GLA2010), Tsukuba (Japan), March 201

Feasibility of high-voltage systems for a very long drift in liquid argon TPCs

Designs of high-voltage (HV) systems for creating a drift electric field in liquid argon TPCs are reviewed. In ongoing experiments systems capable of approx. 100 kV are realised for a drift field of 0.5-1 kV/cm over a length of up to 1.5 m. Two of them having different approaches are presented: (1) the ICARUS-T600 detector having a system consisting of an external power supply, HV feedthroughs and resistive voltage degraders and (2) the ArDM-1t detector having a cryogenic Greinacher HV multiplier inside the liquid argon volume. For a giant scale liquid argon TPC, a system providing 2 MV may be required to attain a drift length of approx. 20 m. Feasibility of such a system is evaluated by extrapolating the existing designs.Comment: 8 pages, 13 figures, to appear in Proc. of 1st International Workshop towards the Giant Liquid Argon Charge Imaging Experiment (GLA2010), Tsukuba (Japan), March 201

A series solution and a fast algorithm for the inversion of the spherical mean Radon transform

An explicit series solution is proposed for the inversion of the spherical mean Radon transform. Such an inversion is required in problems of thermo- and photo- acoustic tomography. Closed-form inversion formulae are currently known only for the case when the centers of the integration spheres lie on a sphere surrounding the support of the unknown function, or on certain unbounded surfaces. Our approach results in an explicit series solution for any closed measuring surface surrounding a region for which the eigenfunctions of the Dirichlet Laplacian are explicitly known - such as, for example, cube, finite cylinder, half-sphere etc. In addition, we present a fast reconstruction algorithm applicable in the case when the detectors (the centers of the integration spheres) lie on a surface of a cube. This algorithm reconsrtucts 3-D images thousands times faster than backprojection-type methods

Stable operation with gain of a double phase Liquid Argon LEM-TPC with a 1 mm thick segmented LEM

In this paper we present results from a test of a small Liquid Argon Large Electron Multiplier Time Projection Chamber (LAr LEM-TPC). This detector concept provides a 3D-tracking and calorimetric device capable of charge amplification, suited for next-generation neutrino detectors and possibly direct Dark Matter searches. During a test of a 3~lt chamber equipped with a 10$\times$10~cm$^2$ readout, cosmic muon data was recorded during three weeks of data taking. A maximum gain of 6.5 was achieved and the liquid argon was kept pure enough to ensure 20~cm drift (O(ppb)~O$_2$ equivalent).Comment: 7 pages, 6 figures, to appear in Proc. of 1st International Workshop towards the Giant Liquid Argon Charge Imaging Experiment (GLA2010), Tsukuba (Japan), March 201

First operation of a double phase LAr Large Electron Multiplier Time Projection Chamber with a two-dimensional projective readout anode

We have previously reported on the construction and successful operation of the novel double phase Liquid Argon Large Electron Multiplier Time Projection Chamber (LAr LEM-TPC). This detector concept provides a 3D-tracking and calorimetric device capable of adjustable charge amplification, a promising readout technology for next-generation neutrino detectors and direct Dark Matter searches. In this paper, we report on the first operation of a LAr LEM-TPC prototype - with an active area of 10$\times$10 cm$^2$ and 21 cm drift length - equipped with a single 1 mm thick LEM amplifying stage and a two dimensional projective readout anode. Cosmic muon events were collected, fully reconstructed and used to characterize the performance of the chamber. The obtained signals provide images of very high quality and the energy loss distributions of minimum ionizing tracks give a direct estimate of the amplification. We find that a stable gain of 27 can be achieved with this detector configuration corresponding to a signal-over-noise ratio larger than 200 for minimum ionizing tracks. The decoupling of the amplification stage and the use of the 2D readout anode offer several advantages which are described in the text.Comment: 25 pages, 17 figure

Exponential instability in the fractional Calder\'on problem

In this note we prove the exponential instability of the fractional Calder\'on problem and thus prove the optimality of the logarithmic stability estimate from \cite{RS17}. In order to infer this result, we follow the strategy introduced by Mandache in \cite{M01} for the standard Calder\'on problem. Here we exploit a close relation between the fractional Calder\'on problem and the classical Poisson operator. Moreover, using the construction of a suitable orthonormal basis, we also prove (almost) optimality of the Runge approximation result for the fractional Laplacian, which was derived in \cite{RS17}. Finally, in one dimension, we show a close relation between the fractional Calder\'on problem and the truncated Hilbert transform.Comment: 17 page