Real-time imaging of the spatial distribution of rf-heating in NMR samples during broadband decoupling

Continuous radio-frequency (rf) irradiation during decoupling and spin-lock periods in NMR pulse sequences may lead to undesired sample heating. Heat-sensitive samples can suffer damage from the sudden temperature rise which cannot be adequately compensated by the temperature control system. Moreover, as the heating is spatially inhomogeneous, higher temperature increases can arise locally than are indicated by the average increase detected by the temperature controller. In this work we present a technique that allows measurement of a real-time 2D-image of the temperature distribution inside an NMR sample during an experiment involving rf-heating. NMR imaging methods have previously been used to project the temperature distribution inside an NMR sample onto a single spatial axis or to acquire steady-state 2D- temperature distributions. The real-time 2D-temperature profiles obtained with our procedure provide much more detailed data. Our results show, that not only inhomogeneous heating but also inhomogeneous sample cooling contribute to the build-up of temperature gradients across the sample. The technique can be used to visualize rf-heating in order to protect sensitive samples and to experimentally test new coil geometries or to guide probehead design.     

Low-E probe for (19)F-(1)H NMR of dilute biological solids

Sample heating induced by radio frequency (RF) irradiation presents a significant challenge to solid state NMR experiments in proteins and other biological systems, causing the sample to dehydrate which may result in distorted spectra and a damaged sample. In this work we describe a large volume, low-E (19)F-(1)H solid state NMR probe, which we developed for the 2D (19)F CPMG studies of dilute membrane proteins in a static and electrically lossy environment at 600MHz field. In (19)FCPMG and related multi-pulse (19)F-(1)H experiments the sample is heated by the conservative electric fields E produced in the sample coil at both (19)F and (1)H frequencies. Instead of using a traditional sample solenoid, our low-E (19)F-(1)H probe utilizes two orthogonal loop-gap resonators in order to minimize the conservative electric fields responsible for sample heating. Absence of the wavelength effects in loop-gap resonators results in homogeneous RF fields and enables the study of large sample volumes, an important feature for the dilute protein preparations. The orthogonal resonators also provide intrinsic isolation between the (19)F and (1)H channels, which is another major challenge for the (19)F-(1)H circuits where Larmor frequencies are only 6% apart. We detail steps to reduce (19)F background signals from the probe, which included careful choice of capacitor lubricants and manufacture of custom non-fluorinated coaxial cables. Application of the probe for two-dimensional (19)F CPMG spectroscopy in oriented lipid membranes is demonstrated with Flufenamic acid (FFA), a non-steroidal anti-inflammatory drug.     

Predicting high harmonic ion cyclotron heating efficiency in Tokamak plasmas

Observations of improved radio frequency (rf) heating efficiency in ITER relevant high-confinement (H-)mode plasmas on the National Spherical Tokamak Experiment are investigated by whole-device linear simulation. The steady-state rf electric field is calculated for various antenna spectra and the results examined for characteristics that correlate with observations of improved or reduced rf heating efficiency. We find that launching toroidal wave numbers that give fast-wave propagation in the scrape-off plasma excites large amplitude (～kV?m(-1)) coaxial standing modes between the confined plasma density pedestal and conducting vessel wall. Qualitative comparison with measurements of the stored plasma energy suggests that these modes are a probable cause of degraded heating efficiency.     

A novel low-E field coil to minimize heating of biological samples in solid-state multinuclear NMR experiments

A novel coil, called Z coil, is presented. Its function is to reduce the strong thermal effects produced by rf heating at high frequencies. The results obtained at 500MHz in a 50 microl sample prove that the Z coil can cope with salt concentrations that are one order of magnitude higher than in traditional solenoidal coils. The evaluation of the rf field is performed by numerical analysis based on first principles and by carrying out rf field measurements. Reduction of rf heating is probed with a DMPC/DHPC membrane prepared in buffers of increasing salt concentrations. The intricate correlation that exists between the magnetic and electric field is presented. It is demonstrated that, in a multiply tuned traditional MAS coil, the rf electric field E(1) cannot be reduced without altering the rf magnetic field. Since the detailed distribution differs when changing the coil geometry, a comparison involving the following three distinct designs is discussed: (1) a regular coil of 5.5 turns, (2) a variable pitch coil with the same number of turns, (3) the new Z coil structure. For each of these coils loaded with samples of different salt concentrations, the nutation fields obtained at a certain power level provide a basis to discuss the impact of the dielectric and conductive losses on the rf efficiency.     

Using low-E resonators to reduce RF heating in biological samples for static solid-state NMR up to 900 MHz

RF heating of solid-state biological samples is known to be a destabilizing factor in high-field NMR experiments that shortens the sample lifetime by continuous dehydration during the high-power cross-polarization and decoupling pulses. In this work, we describe specially designed, large volume, low-E 15N-1H solid-state NMR probes developed for 600 and 900 MHz PISEMA studies of dilute membrane proteins oriented in hydrated and dielectrically lossy lipid bilayers. The probes use an orthogonal coil design in which separate resonators pursue their own aims at the respective frequencies, resulting in a simplified and more efficient matching network. Sample heating at the 1H frequency is minimized by a loop-gap resonator which produces a homogeneous magnetic field B1 with low electric field E. Within the loop-gap resonator, a multi-turn solenoid closely matching the shape of the sample serves as an efficient observe coil. We compare power dissipation in a typical lossy bilayer sample in the new low-E probe and in a previously reported 15N-1H probe which uses a double-tuned 4-turn solenoid. RF loss in the sample is measured in each probe by observing changes in the 1H 360 degrees pulse lengths. For the same values of 1H B1 field, sample heating in the new probe was found to be smaller by an order of magnitude. Applications of the low-E design to the PISEMA study of membrane proteins in their native hydrated bilayer environment are demonstrated at 600 and 900 MHz.     

Hydration-optimized oriented phospholipid bilayer samples for solid-state NMR structural studies of membrane proteins

The preparation of oriented, hydration-optimized lipid bilayer samples, for NMR structure determination of membrane proteins, is described. The samples consist of planar phospholipid bilayers, containing membrane proteins, that are oriented on single pairs of glass slides, and are placed in the coil of the NMR probe with the bilayer plane perpendicular to the direction of the magnetic field. Lipid bilayers provide a medium that closely resembles the biological membrane, and sample orientation both preserves the intrinsic membrane-defined directional quality of membrane proteins, and provides the mechanism for resonance line narrowing. The hydration-optimized samples overcome some of the difficulties associated with multi-dimensional, high-resolution, solid-state NMR spectroscopy of membrane proteins. These samples have greater stability over the course of multi-dimensional NMR experiments, they have lower sample conductance for greater rf power efficiency, and enable greater rf coil filling factors to be obtained for improved experimental sensitivity. Sample preparation is illustrated for the membrane protein CHIF (channel inducing factor), a member of the FXYD family of ion transport regulators.     

The utility of phase alternated pulses for the measurement of dipolar couplings in 2D-SLF experiments

The measurement of hetero-nuclear dipolar coupling using two-dimensional separated local field (SLF-2D) NMR experiments is a powerful technique for the determination of the structure and dynamics of molecules in the solid state and in liquid crystals. However, the experiment is sensitive to a number of factors such as the Hartmann–Hahn match condition, proton frequency off-set and rf heating. It is shown here that by the use of phase alternated pulses during spin-exchange the effect of rf mismatch on the dipolar coupling measurement can be compensated over a wide range of off-sets. Phase alternation together with time and amplitude modulation has also been considered and incorporated into a pulse scheme that combines spin exchange with homonuclear spin decoupling based on magic sandwich sequence and named as SAMPI4. Such time and amplitude averaged nutation experiments use relatively low rf power and generate less sample heating. One of these schemes has been applied on liquid crystal samples and is observed to perform well and yield spectra with high resolution.     

Abnormal heating of low-energy electrons in low-pressure capacitively coupled discharges

In low-pressure capacitively coupled plasmas, high-energy electrons are collisionlessly heated by large rf fields in the sheaths while low-energy electrons are confined in the bulk plasma by the ambipolar potential. Low-energy electrons are typically inefficiently heated due to their low collisionality and the weak rf electric field present in the bulk. It is shown, however, that as a result of the nonlinear interaction between the electron motion and the weak rf field present in the bulk, low-energy electrons can be efficiently heated. Electrons in the bulk that bounce inside the electrostatic potential well with a frequency equal to the rf excitation frequency are efficiently heated by the coherent interaction with the rf field. This resonant collisionless heating can be very efficient and manifest itself as a plateau in the electron energy probability function.     

NMR spectra under skin-effect conditions at ultralow temperatures

An investigation based on the coupled Maxwell-Bloch equations for a system of equivalent exchange-coupled spins is performed in order to explain a number of features of NMR spectra obtained in metals by Fourier-transforming of the free-induction decay at ultralow temperatures. Small angles of tilting of the nuclear magnetization by the exciting rf field are considered. It is shown that the free precession inherits the nonuniformity in the distribution of the rf field and the magnetization produced at the excitation stage inside the sample on account of the skin effect. As a result, the NMR spectrum is found to consist of a set of peaks—signals due to standing spin waves. However, such a spectrum can be observed only when the detuning of the exciting rf field is sufficiently large relative to the Larmor frequency of the spins. Otherwise, the rf field does not penetrate into the sample because of strong absorption by the spins. If the detuning is large, the dispersion signal and part of the NMR absorption signal are proportional to the equilibrium magnetization to the power 3/2. Such behavior is expected at low temperatures so that the coupling of the magnetization with the rf field is strong. The results obtained qualitatively explain the experimentally observed characteristics of the NMR spectra: the presence of kinks and structure of the NMR lines, the dependence of the shape and intensity of the spectrum on the detuning of the exciting rf field, and the nonlinear dependence of the nuclear susceptibility on the reciprocal of the sample temperature. Zh. éksp. Teor. Fiz. 114, 1836–1847 (November 1998)     

Low-Q cavities for high-power gyrotrons

The parameters of free oscillations in gyrotron resonators with a lowered reflection from the diffractive energy output for the purpose of reducing ohmic heating by rf power loss have been calculated. A gyrotron with such a cavity has been studied experimentally. The gyrotron had an efficiency of more than 45% with an output of 350 to 700 kW when operating in the 3.6-mm H_11,3 mode.Institute of Applied Physics, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 3, pp. 381–386, March, 1994.     

Inductance of rf-wave-heated plasmas

The inductance of rf-wave-heated plasmas is derived. This inductance represents the inductance of fast electrons located in a plateau during their acceleration due to electric field or deceleration due to collisions and electric field. This inductance has been calculated for small electric fields from the two-dimensional Fokker-Planck equation as the flux crossing the surface of critical energy mv(2)(ph)/2 in the velocity space. The new expression may be important for radio-frequency current drive ramp-up, current drive efficiency, current profile control, and so on in tokamaks. This inductance may be incorporated into transport codes that study plasma heating by rf waves.     

Heating of gadolinium plasma ions by the ion cyclotron resonance method

Resonance rf heating of gadolinium plasma ions is calculated in the configuration when an electric field travels along a permanent magnetic field and simultaneously rotates in the direction normal to the latter. Two model functions are taken as initial ion distribution functions over longitudinal velocities: one is a linear function of the velocity in the low velocity range and the other is a shifted semi-Maxwellian function. The ion transverse velocity distribution function is calculated under the assumption that the initial “transverse” distribution function is Maxwellian with a temperature of 5 eV. Ion fluxes toward collector plates are calculated by integrating the total distribution function over the allowed ranges of longitudinal and transverse velocities and transverse coordinates of the guiding center of the ions before the collector. The calculation is performed as applied to the ¹⁵⁷Gd target isotope and its two nearest neighbors. The effect of the longitudinal temperature on the width of the heating efficiency resonance line and of the longitudinal magnetic field on the ion heating selectivity is studied. Also, the influence of the longitudinal wavenumber of the warming traveling electric field on the selectivity of an ion cyclotron resonance reactor is investigated. The heating efficiency is estimated from the frequency dependence of the fraction of ions heated to an energy above a given value.     

A low-E magic angle spinning probe for biological solid state NMR at 750 MHz

Crossed-coil NMR probes are a useful tool for reducing sample heating for biological solid state NMR. In a crossed-coil probe, the higher frequency ¹H field, which is the primary source of sample heating in conventional probes, is produced by a separate low-inductance resonator. Because a smaller driving voltage is required, the electric field across the sample and the resultant heating is reduced. In this work we describe the development of a magic angle spinning (MAS) solid state NMR probe utilizing a dual resonator. This dual resonator approach, referred to as “low-E,” was originally developed to reduce heating in samples of mechanically aligned membranes. The study of inherently dilute systems, such as proteins in lipid bilayers, via MAS techniques requires large sample volumes at high field to obtain spectra with adequate signal-to-noise ratio under physiologically relevant conditions. With the low-E approach, we are able to obtain homogeneous and sufficiently strong radiofrequency fields for both ¹H and ¹³C frequencies in a 4 mm probe with a ¹H frequency of 750 MHz. The performance of the probe using windowless dipolar recoupling sequences is demonstrated on model compounds as well as membrane-embedded peptides.     

基于开口环阵列结构的表面晶格共振产生及二次谐波增强

理论研究了二维周期排列的金开口环谐振器的磁共振模式与周期阵列的衍射模式发生强耦合所需满足的条件及其对二次谐波产生效率的影响.通过控制阵列结构在x和y方向的周期大小,使得衍射模式只在其中一个方向产生,当衍射模式的电场方向与入射光电场偏振方向一致时,衍射模式才会与开口环谐振器的磁共振模式发生强耦合作用,产生表面晶格共振进而实现近场场增强.在此基础上,进一步计算了金开口环谐振器阵列的二次谐波产生效率,随着阵列周期逐渐增大,即开口环谐振器的数密度减小,二次谐波强度呈现先增加后降低的趋势,当开口环谐振器数密度降为原来的1/4左右时,二次谐波强度可以增强2倍以上.本文的研究为金属超表面二次谐波产生效率的提高提供了一种新的可能途径.     

Design and application of robust rf pulses for toroid cavity NMR spectroscopy

We present robust radio frequency (rf) pulses that tolerate a factor of six inhomogeneity in the B? field, significantly enhancing the potential of toroid cavity resonators for NMR spectroscopic applications. Both point-to-point (PP) and unitary rotation (UR) pulses were optimized for excitation, inversion, and refocusing using the gradient ascent pulse engineering (GRAPE) algorithm based on optimal control theory. In addition, the optimized parameterization (OP) algorithm applied to the adiabatic BIR-4 UR pulse scheme enabled ultra-short (50 μs) pulses with acceptable performance compared to standard implementations. OP also discovered a new class of non-adiabatic pulse shapes with improved performance within the BIR-4 framework. However, none of the OP-BIR4 pulses are competitive with the more generally optimized UR pulses. The advantages of the new pulses are demonstrated in simulations and experiments. In particular, the DQF COSY result presented here represents the first implementation of 2D NMR spectroscopy using a toroid probe.     

新型的高温超导薄膜梳齿谐振器

本文报导了一种新型结构的高温超导薄膜梳齿谐振器.我们通过改变谐振器梳齿的长度,使谐振器的谐振频率可以从800MHz到1300MHz左右,这正是我们研制的Hi-Tc rf SQUID所需要的两个频段.我们对这种新型谐振器的谐振频率与几何尺寸的关系进行了数值拟合.测试了使用该种新型谐振器的Hi-Tc rf SQUID的噪声.     

Numerical solutions for single passage NMR on nuclei experiencing small electric quadrupole interactions

The adiabatic rapid-passage NMR equations are numerically solved for a small additional quadrupole interaction. The full range of the ratio of rf interaction strengths to quadrupole interactions strengths is considered for any electric field gradient orientation. The results forI=1 are particularly easy to describe and are used to predict the single-passage results for different orientations of the electric field gradient with respect to the static magnetic field.     

Optimal control in NMR spectroscopy: Numerical implementation in SIMPSON

We present the implementation of optimal control into the open source simulation package SIMPSON for development and optimization of nuclear magnetic resonance experiments for a wide range of applications, including liquid- and solid-state NMR, magnetic resonance imaging, quantum computation, and combinations between NMR and other spectroscopies. Optimal control enables efficient optimization of NMR experiments in terms of amplitudes, phases, offsets etc. for hundreds-to-thousands of pulses to fully exploit the experimentally available high degree of freedom in pulse sequences to combat variations/limitations in experimental or spin system parameters or design experiments with specific properties typically not covered as easily by standard design procedures. This facilitates straightforward optimization of experiments under consideration of rf and static field inhomogeneities, limitations in available or desired rf field strengths (e.g., for reduction of sample heating), spread in resonance offsets or coupling parameters, variations in spin systems etc. to meet the actual experimental conditions as close as possible. The paper provides a brief account on the relevant theory and in particular the computational interface relevant for optimization of state-to-state transfer (on the density operator level) and the effective Hamiltonian on the level of propagators along with several representative examples within liquid- and solid-state NMR spectroscopy.     

Separation of rf-collapse effect from heat-narrowing in permalloy foil samples

In rf-collapse of hyperfine field of soft ferromagnetic metal samples, ambiguity arises due to eddy current heating that rf field induces, which progressively narrows the Hfs-spectrum with increasing rf power, ultimately reducing it to a single unsplit line above Curie point. We report experiments with perforated permalloy foils. In these, path for local eddy current loops are broken reducing the eddy current heating, as against only removal of heat generated, in many previous collapse studies. The effect of rf-collapse can be demonstrated conclusively when it is seen in conjuction with presence of internal magnetic field. For this purpose, we took spectra in switched rf field experiments, where rf switch-OFF and ON cycle was synchronised to the two halves of velocity sweep. Results clearly shows Hfs-spectrum when rf field is OFF and rf-collapse when rf field is ON.     

The generation of intense radiofrequency fields in microcoils

Large amplitude radiofrequency (rf) fields hold great promise in wide line NMR where it becomes possible to excite the full breadth of the line in a quantitative fashion. Applications in quadrupole NMR and in NMR of paramagnetic systems benefit greatly from intense fields. Spin manipulations in multiple quantum NMR experiments, specifically, the generation of multiple quantum coherence in MQ NMR, are more efficiently produced using intense rf fields. In this work we describe a microcoil probe that produces an rf field of 25 MHz, more than five times larger than the greatest rf field reported in the literature. We accomplish this in a robust, 127 microm diameter solenoid coil using 1 kW of rf power.