Adiabatic and broadband pulses

An alternative and highly efficient approach to spin inversion is offered by the so-called adiabatic pulses [12, 13]. Rather than pulses applied at a single frequency, these employ a 

Adiabatic pulses are described by their frequency sweep and amplitude profile, which, when combined with the peak rf amplitude cc max), defines the total power of the pulse. The total frequency range, AF, over which the pulse sweeps is commonly many tens of kilohertz and pulse durations, T, are typically of the order of 1 ms, corresponding to frequency sweep rates of 10-100 MHz/s. The degree to which the adiabatic condition is satisfied for the pulse is quantified by the adiabaticity factor Q 

In the case of the commonly employed linear (i.e. constant rate) frequency sweep, the term dAuj/dt may be equated with the sweep rate of the pulse, AF/T, and the on-resonance rf field defines the maximum amplitude for the pulse cci( iax) rad/s, which one can write more usefully in terms of 7Si(i ax) 

From this expression, one calculates the maximum peak amplitude of the adiabatic pulse 7Bi(max) for a chosen value of Qq, which must usually be significantly larger than unity, and is typically set to 3-5 for most applications. Thus, a 0.5-ms adiabatic pulse sweeping over a 

60-kHz window requires a peak amplitude of 9.77 kHz with go of 5, which corresponds to the power of a 25.6- is-hard 90° pulse. Such calculations are performed most conveniently within the software tools provided with spectrometer software, and their experimental implementation is most readily achieved on instruments with linear amplifiers where the necessary rf attenuation may be calculated directly from hard-pulse calihrations (see Section 3.5.1). 

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