# floquet.m

Floquet magic angle spinning context. This function generates Floquet Hamiltonian at a particular orientation, relaxation superoperator, kinetics superoperator, applies the necessary offsets, updates the parameter set, and passes all of that to the pulse sequence, which should be supplied as a handle. Parallel powder averaging is applied.

## Contents

## Syntax

answer=floquet(spin_system,@pulse_sequence,parameters,assumptions)

## Arguments

@pulse_sequence - pulse sequence function handle parameters.rate - spinning rate in Hz. Positive numbers for JEOL, negative for Varian and Bruker due to different rotation directions. parameters.axis - spinning axis, given as a normalized 3-element vector parameters.spins - a cell array giving the spins that the pulse sequence involves, e.g. {'1H','13C'} parameters.offset - a cell array giving transmitter off- sets in Hz on each of the spins listed in parameters.spins array parameters.max_rank - maximum harmonic rank to retain in the solution (increase till conver- gence is achieved, approximately equal to the number of spinning si- debands in the spectrum) parameters.grid - powder averaging grid parameters.sum_up - when set to 1 (default), returns the powder average. When set to 0, returns individual answers for each point in the powder as a cell array. parameters.* - additional subfields may be required by your pulse sequence - check its documentation page

The parameters structure is passed to the pulse sequence with the following additional parameters set:

parameters.spc_dim - matrix dimension for the spatial dynamics subspace parameters.spn_dim - matrix dimension for the spin dynamics subspace

## Outputs

This function returns the powder average of whatever it is that the pulse sequence returns, or the components of that powder average, if the sum_up flag is cleared.

## Examples

The following example files in the Spinach example set make use of this context function:

**nmr_solids/mas_powder_trp_floquet.m** - large-scale simulation of tryptophan 13C MAS NMR

**nmr_solids/mas_powder_gly_floquet.m** - glycine 13C MAS NMR spectrum

**nmr_solids/mas_powder_suc_floquet.m** - large-scale simulation of sucrose 13C MAS NMR

**nmr_solids/mas_powder_ala_floquet.m** - alanine 13C MAS NMR spectrum

**nmr_solids/mas_powder_nqi_floquet.m** - deuterium NQI MAS NMR, no second-order rotating frame corrections

**nmr_solids/mas_powder_dip_floquet.m** - MAS NMR on a pair of dipole coupled spins

**nmr_solids/mas_powder_csa_floquet.m** - MAS NMR on a simple system with a CSA

## Notes

- The choice of the rank depends on the spinning rate (the slower the spinning, the greater ranks are required). The rank should be set approximately equal to the expected number of spinning sidebands. Increase till the answer stops changing.
- The state projector assumes a powder - single crystal MAS is not supported, use singlerot.m instead.
- Perturbative corrections to the rotating frame transformation are not supported - use singlerot.m instead.
- The function supports parallel processing via Matlab's Distributed Computing Toolbox - different system orientations are evaluated on different labs.

## See also

powder.m, liquid.m, roadmap.m, singlerot.m, doublerot.m, imaging.m, gridfree.m, crystal.m

*Version 2.2, authors: Ilya Kuprov, Luke Edwards*