We describe the construction of stepped-pressure equilibria as extrema of a
multi-region, relaxed magnetohydrodynamic (MHD) energy functional that combines
elements of ideal MHD and Taylor relaxation, and which we call MRXMHD.
The model is compatible with Hamiltonian chaos theory and allows the
three-dimensional MHD equilibrium problem to be formulated in a well-posed
manner suitable for computation.
The energy-functional is discretized using a mixed finite-element, Fourier
representation for the magnetic vector potential and the equilibrium geometry;
and numerical solutions are constructed using the stepped-pressure equilibrium
code, SPEC.
Convergence studies with respect to radial and Fourier resolution are
presented
XMDS2 is a cross-platform, GPL-licensed, open source package for numerically integrating initial value problems that range from a single ordinary differential equation up to systems of coupled stochastic partial differential equations. The equations are described in a high-level XML-based script, and the package generates low-level optionally parallelised C++ code for the efficient solution of those equations. It combines the advantages of high-level simulations, namely fast and low-error development, with the speed, portability and scalability of hand-written code. XMDS2 is a complete redesign of the XMDS package, and features support for a much wider problem space while also producing faster code.
We present a cold-atom gravimeter operating with a sample of Bose-condensed 87 Rb atoms. Using a Mach-Zehnder configuration with the two arms separated by a two-photon Bragg transition, we observe interference fringes with a visibility of (83 ± 6)% at T = 3 ms. We exploit large momentum transfer (LMT) beam splitting to increase the enclosed space-time area of the interferometer using higher-order Bragg transitions and Bloch oscillations. We also compare fringes from condensed and thermal sources and observe a reduced visibility of (58 ± 4)% for the thermal source. We suspect the loss in visibility is caused partly by wave-front aberrations, to which the thermal source is more susceptible due to its larger transverse momentum spread. Finally, we discuss briefly the potential advantages of using a coherent atomic source for LMT, and we present a simple mean-field model to demonstrate that with currently available experimental parameters, interaction-induced dephasing will not limit the sensitivity of inertial measurements using freely falling, coherent atomic sources.
We present a precision gravimeter based on coherent Bragg diffraction of freely falling cold atoms. Traditionally, atomic gravimeters have used stimulated Raman transitions to separate clouds in momentum space by driving transitions between two internal atomic states. Bragg interferometers utilize only a single internal state, and can therefore be less susceptible to environmental perturbations. Here we show that atoms extracted from a magneto-optical trap using an accelerating optical lattice are a suitable source for a Bragg atom interferometer, allowing efficient beamsplitting and subsequent separation of momentum states for detection. Despite the inherently multi-state nature of atom diffraction, we are able to build a Mach-Zehnder interferometer using Bragg scattering which achieves a sensitivity to the gravitational acceleration of g/g = 2.7 × 10 −9 with an integration time of 1000 s. The device can also be converted to a gravity gradiometer by a simple modification of the light pulse sequence.
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