E-H-Zyklotronechos in Plasmen

A new echo type with free electrons in a slight inhomogeneous magnetic field excited by one electric and one magnetic pulse is calculated. Thus features of cyclotron echos and spin echoes are combined. The first electric pulse accelerates all (cold) particles to the same velocity as in the case of usual cyclotron echoes. The second magnetic pulse (at t = τ) rotates the plane of precession in phase space, quite in analogy to the motion of magnetic moments in the case of spin echoes. The echo arises at t = 2τ. The E-H echoes make relaxation and diffusion measurements in plasmas possible, using the methods proved useful in spin echo technique. There are no complications as in the case of E-E cyclotron echoes which are based on the fact that a velocity-dependent collision frequency is necessary for the nonlinearity of that echo mechanism.     

Nuclear magnetic resonance in inhomogeneous magnetic fields

The response of the spin system has been investigated by numerical simulations in the case of a nuclear magnetic resonance (NMR) experiment performed in inhomogeneous static and radiofrequency fields. The particular case of the NMR-MOUSE was considered. The static field and the component of the radiofrequency field perpendicular to the static field were evaluated as well as the spatial distribution of the maximum NMR signal detected by the surface coil. The NMR response to various pulse sequences was evaluated numerically for the case of an ensemble of isolated spins (1/2). The behavior of the echo train in Carr-Purcell-like pulse sequences used for measurements of transverse relaxation and self-diffusion was simulated and compared with the experiment. The echo train is shown to behave qualitatively differently depending on the particular phase schemes used in these pulse sequences. Different echo trains are obtained, because of the different superposition of Hahn and stimulated echoes forming mixed echoes as a result of the spatial distribution of pulse flip angles. The superposition of Hahn and stimulated echoes originating from different spatial regions leads to distortions of the mixed echoes in intensity, shape, and phase. The volume selection produced by Carr-Purcell-like pulse sequences is also investigated for the NMR-MOUSE. The developed numerical simulation procedure is useful for understanding a variety of experiments performed with the NMR-MOUSE and for improving its performance. Copyright 2000 Academic Press.     

Multiecho processing by an echolocating dolphin

Bottlenose dolphins (Tursiops truncatus) use short, wideband pulses for echolocation. Individual waveforms have high-range resolution capability but are relatively insensitive to range rate. Signal-to-noise ratio (SNR) is not greatly improved by pulse compression because each waveform has small time-bandwidth product. The dolphin, however, often uses many pulses to interrogate a target, and could use multipulse processing to combine the resulting echoes. Multipulse processing could mitigate the small SNR improvement from pulse compression, and could greatly improve range-rate estimation, moving target indication, range tracking, and acoustic imaging. All these hypothetical capabilities depend upon the animal's ability to combine multiple echoes for detection and/or estimation. An experiment to test multiecho processing in a dolphin measured detection of a stationary target when the number N of available target echoes was increased, using synthetic echoes. The SNR required for detection decreased as the number of available echoes increased, as expected for multiecho processing. A receiver that sums binary-quantized data samples from multiple echoes closely models the N dependence of the SNR required by the dolphin. Such a receiver has distribution-tolerant (nonparametric) properties that make it robust in environments with nonstationary and/or non-Gaussian noise, such as the pulses created by snapping shrimp.     

CPMG echo amplitudes with arbitrary refocusing angle: explicit expressions, asymptotic behavior, approximations

Exact explicit analytical expression for echoes in the Carr–Purcell–Meiboom–Gill sequence with arbitrary excitation and refocusing angles and resonance offset of RF pulses was obtained, employing the generating functions formalism developed earlier by authors. Asymptotic form and analytical approximation for echoes were derived in an elegant way and analyzed in details. In particular, it was shown that depending on T₁, T₂ and parameters of the pulse sequence, oscillatory behavior of echoes can take place. Accuracy of asymptotic forms and approximations were tested by comparison with exactly calculated echo amplitudes. Besides, it was shown, that the generating function approach can be applied to the consideration of terminated pulse sequences, when after-pulses echoes are registered.     

Solomon echoes for spin 7/2 by soft pulse excitation

Solomon echoes are calculated for spin 7/2 in solids taking into account the first-order quadrupolar interaction while the pulses are on. The computation is performed using the algebraic computer program ‘MAPLE’. Fifteen echoes are predicted and the amplitude of each echo is calculated. Each satellite transition produces five echoes whereas no echo is detected for the central transition. Among these echoes, six are ‘forbidden’ which are a result of the refocusing of exclusively multiple quantum coherences which are developed during the first pulse. These echoes cannot be predicted by a calculation based upon ‘hard’ pulse excitation. The results are valid for any ratio of the quadrupolar coupling to the frequency of the RF field (ω_Q/ω₁).     

SAR reduced pulse sequences

Three techniques were considered for reducing the RF (radiofrequency) power deposition in the body while maintaining scan time efficiency: reducing the RF peak amplitude while increasing the pulse width, substituting gradient echoes for spin echoes, and reducing the flip angle of the phase reversal pulse. The use of gradient echoes was found to be the most efficient means to reduce the power delivered to the patient and to obtain rapid data acquisition. The effect upon SAR (specific absorption rate) and SNR (signal-to-noise ratio) was demonstrated on a phantom when the phase reversal pulse was reduced from the standard 180 degrees to 90 degrees. Data in the body indicated a fairly constant SNR down to a refocusing flip angle between 110 degrees and 135 degrees. An initial clinical evaluation was performed at three institutions using the method of reducing the flip angle of the phase reversal pulse. The scan with theta = 120 degrees was rated by readers in a blinded study as having acceptable diagnostic image quality while the 135 degrees scan had comparable image quality to a conventional 90 degrees - 180 degrees pulse sequence. The use of reduced phase reversal pulses was seen as an efficient protocol to obtain T1-weighted images at rapid data rates while reducing the power delivered to the body by about 40%.     

Multiple echoes, multiple quantum coherence, and the dipolar field: demonstrating the significance of higher order terms in the equilibrium density matrix.

It is well known that dipolar field effects lead to multiple spin echoes in a simple two-RF pulse experiment (the MSE experiment). We show here that coherence transfer echoes (which identify the existence of multiple quantum coherences in liquid NMR) and multiple spin echoes have a common origin. Using density matrix theory we have calculated the phase and timing of multiple spin echoes from all quadrature phase combinations of RF pulses. We show for the MSE experiment that there is a one-to-one correspondence between the time domain echo order and the multiple quantum coherence order. The experimental confirmation of these phase predictions shows that multiple spin echoes provide independent evidence for the breakdown of the high temperature approximation as proposed by Warren et al. (Science 262, 2005 (1993)).     

Dephasing processes as studied by two pulse photon echoes and photochemically accumulated echoes: The question of spectral diffusion in a doped organic polymer matrix

Two pulse photon echoes (2PPE) and photochemically accumulated stimulated photon echoes (PASPE) were measured under identical conditions for the system octaethylporphin in a polystyrene matrix. Experiments at 1.9 K show that both echoes have a different decay behavior. Whereas the 2PPE-signal decays with a time constant of 1300 ps, the PASPE-signal decays faster with a time constant of 600 ps. The different temporal behavior of both signals is tentatively attributed to spectral diffusion.     

强电磁脉冲信号激励下复杂目标的散射

用时域有限差分法仿真了某飞行器缩比模型及该模型涂敷雷达吸波材料的散射特性,得到了鼻锥方向、侧向和后向ns级脉冲激励下模型的时域响应和频域雷达散射截面;并在外场用ns级脉冲源进行了该金属模型的探测实验。仿真与外场实验结果均得到了模型的鼻锥方向回波幅度最小,侧向最大;鼻锥方向回波脉宽最宽,侧向最窄的结论。研究结果表明：外形隐身和材料隐身对ns或亚ns级窄脉冲的隐身效果不明显,ns或亚ns级窄脉冲能发现和识别隐身目标。     

Photon echo in superradiant media

It was shown that if an additional emission of a superradiance pulse by a medium occurs after an initial exciting pulse, two-pulse photon echoes are formed at a different frequencies and at a new time as compared to an ordinary medium. Conditions for the spatial synchronism of these photon echo were found.     

Two-pulse nutation echoes generated by gradients of the radiofrequency amplitude and of the main magnetic field

A two-pulse NMR nutation spectroscopy scheme is suggested that leads to a new type of spin echoes. The amplitude of the radiofrequency (RF) pulses as well as the external magnetic field are assumed to be subject to gradients G(1) and G(0), respectively, in the same but otherwise arbitrary direction. Multiple echoes are predicted and observed at times k(G(1)/G(0))tau(1) and tau -/+ k(G(1)/G(0))tau(1) (k = 1, 2, 3, ...) after the second RF pulse, where tau(1) represents the radiofrequency pulse duration, and tau is the spacing of the RF pulses. Based on these echoes, a method for diffusion measurements is proposed that simultaneously provides the spin-lattice relaxation time and the self-diffusion coefficient.     

强电磁脉冲信号激励下复杂目标的散射

 用时域有限差分法仿真了某飞行器缩比模型及该模型涂敷雷达吸波材料的散射特性,得到了鼻锥方向、侧向和后向ns级脉冲激励下模型的时域响应和频域雷达散射截面;并在外场用ns级脉冲源进行了该金属模型的探测实验。仿真与外场实验结果均得到了模型的鼻锥方向回波幅度最小,侧向最大;鼻锥方向回波脉宽最宽,侧向最窄的结论。研究结果表明：外形隐身和材料隐身对ns或亚ns级窄脉冲的隐身效果不明显,ns或亚ns级窄脉冲能发现和识别隐身目标。     

Double PGSE NMR with Stimulated Echoes: Phase Cycles for the Selection of Desired Encoding

When two pairs of position-encoding pulses are used in a pulsed gradient spin echo (PGSE) NMR experiment, it is possible to examine velocity fluctuations. The one-dimensional version of double PGSE NMR uses identical pulse pairs whose amplitudes are stepped simultaneously. In the two-dimensional version (VEXSY) the pulse pairs are stepped independently, resulting in a velocity exchange spectrum. A key limitation in such experiments is transverse relaxation, so that stimulated echoes are often used as the method of choice. It is shown here that the use of stimulated echoes results in a superposition of signals arising from different magnetization pathways such that the spin phases may reflect both the sum and difference of displacements over the pulse pair encoding times, as well as the displacement over the exchange time between the pulse pairs. A phase cycle scheme that selects desired encodings as required is demonstrated.     

Physical mechanisms of spin echoes. I. Two-pulse locked echo

The locked echo is the result of the application, to an inhomogeneously-broadened system, of a pulse sequence consisting of a short π/2 pulse, a free evolution period of length r and a long pulse with high turning angle (HTA). In this paper the nature and features of the signal detected after such a pulse sequence are reported upon by analysing the underlying physical mechanisms in the framework of the density operator formalism. It is found that the total signal does not contain any contribution from Free Induction Decay (FID)-like or anti-echo signals but comprises a group of several distinct echoes: the true simultaneous locked echo, arising from locked magnetization, and two or three non-simultaneous, oscillatory echoes similar to those observed in the single-pulse experiment. Properties of these echoes are deduced from the structure of the density operator at the end of the experiment. Extensive numerical simulations provide independent evidence of the correctness of the developed theory, display the variety of patterns shown by the locked echo when experimental conditions are changed, and also permit one to investigate the locked echo shape beyond the approximations introduced in the theory.     

Correlation echoes in the stochastic excitation of inhomogeneously broadened two-level systems

The third-order cross-correlations between a free induction signal of an inhomogeneously broadened two-level system and white Gaussian noise exciting this system are studied. The temporal properties of the third-order cross-correlation functions are found to correspond to the characteristics of ordinary two-and three-pulse spin and light (photon) echoes excited by determinate radio pulses. The nonlinear properties of correlation echoes are studied as functions of the noise pulse parameters. It is established that the correlation echo amplitude is determined not only by the noise pulse parameters but also by the position on the time axis of the noise counts that form the given type of echo. Finally, the behavior of the spin and light correlation echoes in the appropriate ranges is discussed. Zh. éksp. Teor. Fiz. 112, 63–77 (July 1997)     

Quantitative diffusion coefficient maps using fast spin-echo MRI

In this work, we have evaluated the performance of a diffusion-sensitive fast spin-echo (FSE) pulse sequence. The proposed pulse sequence utilises velocity-compensating diffusion-encoding gradients and includes the collection of navigator echoes. Spoiler gradients were inserted in the slice-selecting direction to minimise effects from stimulated echoes. Calculations of the b values showed that cross-terms between imaging gradients and diffusion gradients only led to a marginal increase of b values. Pixel-wise calculation of apparent diffusion coefficient (ADC) maps was performed numerically, considering cross-terms between diffusion-encoding and imaging gradients. The sequences investigated used echo train lengths of 16, 8 and 4 echoes and were encoded in either the slice-, frequency- or phase-encoding direction. In order to allow for higher b values a pulse-sequence version using non-motion compensating diffusion-encoding gradients was written. Phantom measurements were performed and the diffusion coefficients of water and acetone were reasonable. Seven healthy volunteers (age 28–50 years) were examined and apparent diffusion coefficient values agreed well with expected values. Diffusion-weighted images, apparent diffusion coefficient maps and images corresponding to the trace of the diffusion tensor of good quality were retrieved in vivo.     

Grating spin echoes

Single-quantum proton spin coherences produced by a single radio-frequency pulse and evolving in a spatially modulated, external magnetic field were examined theoretically and experimentally in water. It is shown that the coherences are multiply refocused in the form of “grating echoes”. The theoretical treatment describes and explains the phenomena in detail. The fact that this sort of new and unconventional spin echoes can be observed sheds new light on our understanding of other spin coherence phenomena such as the so-called “multiple echoes” first described by G. Deville, M. Bernier, J. M. Delrieux (Phys. Rev. B 19, 5666, 1979).     

水中有限弹性圆柱的窄脉冲回波响应与螺旋表面绕行波

用严格的解析方法求解有限长弹性柱的声散射问题是困难的,而近似的数值计算方法又缺乏物理的直观性.本文提出采用弹性螺旋表面波的声激励和再辐射理论分析模型,对入射声波方向在正横附近一定角度范围内(约±30°)有限弹性圆柱的脉冲回波响应作了分析,建立了用以估算回波时序、幅度和共振模式的基本关系式.给出了目标弹性特性与回波响应的直观物理联系。在水池中,实测了厚壁中空钢柱和铝柱的脉冲响应,实测脉冲回波时序与理论预报结果基本相符。     

Acoustic scattering from double-diffusive microstructure

Laboratory measurements of high-frequency broadband acoustic backscattering (200-600 kHz) from the diffusive regime of double-diffusive microstructure have been performed. This type of microstructure, which was characterized using direct microstructure and optical shadowgraph techniques, is identified by sharp density and sound speed interfaces separating well-mixed layers. Vertical acoustic backscattering measurements were performed for a range of physical parameters controlling the double-diffusive microstructure. The echoes have been analyzed in both the frequency domain, providing information on the spectral response of the scattering, and in the time domain, using pulse compression techniques. High levels of variability were observed, associated with interface oscillations and turbulent plumes, with many echoes showing significant spectral structure. Acoustic estimates of interface thickness (1-3 cm), obtained for the echoes with exactly two peaks in the compressed pulse output, were in good agreement with estimates based on direct microstructure and optical shadowgraph measurements. Predictions based on a one-dimensional weak-scattering model that includes the actual density and sound speed profiles agree reasonably with the measured scattering. A remote-sensing tool for mapping oceanic microstructure, such as high-frequency broadband acoustic scattering, could lead to a better understanding of the extent and evolution of double-diffusive layering, and to the importance of double diffusion to oceanic mixing.     

Electron spin-echo experiments in photo-excited triplet states in an external magnetic field

Electron spin-echo experiments in the photo-excited triplet states of quinoxaline-d₆ and naphthalene-d₈ at 1·2 K in an external magnetic field are presented. These include two-pulse Hahn echoes, three-pulse stimulated echoes and Carr-Purcell pulse-echo trains. The decay of the Hahn and stimulated echoes as a function of pulse interval yields measures of the spin relaxation times. Furthermore, the Hahn echo is used to obtain E.P.R. line shapes and the dynamics of the triplet sublevel populations. The angular dependence of the Hahn echo is also investigated. The Hahn echo decay time and decay modulation suggest the kind of role played by nuclear spins in the loss of electron spin phase coherence. Some promising characteristics of the pulse method are discussed.