Intrinsic Spin Resonance Research Articles

Studies of the spin coherence time of protons at COSY

The search for the Electric Dipole Moments (EDM) of charged particles in storage rings necessitates polarized beams with long Spin Coherence Time (SCT) of the circulating beam. The SCT is the time during which the RMS spread of the orientation of spins of all particles in the bunch reaches one radian. A long SCT is needed to observe the coherent effect of a polarization build-up induced by the EDM. For deuterons the SCT of 1000 s has been achieved at the COoler SYnchrotron COSY (Jülich, Germany). Accomplishing such long SCT for protons is far more challenging due to their higher anomalous magnetic moment, but essential for the planned EDM experiments. It has been shown that for protons the SCT is strongly influenced by nearby intrinsic and integer spin resonances. The strengths of the latter have been calculated for a typical optics setting of COSY and the overall influence on the SCT was predicted. In addition, the efficiency of proton spin flipping with an RF solenoid from initially vertical direction into the ring plane is also investigated.

Booster free from spin resonance for future 100-km-scale circular e+e− colliders

Acceleration of polarized electron~(positron) beams in a booster synchrotron may suffer from depolarization due to crossings of many spin depolarization resonances, which could limit its applications. We have studied the spin depolarization resonance structure of a 100~km scale booster lattice of the Circular Electron Positron Collider~(CEPC). The lattice has 8 arc regions with hundreds of FODO cells, interleaved with straight sections, which leads to a high periodicity. Our analysis shows the contributions to the strength of intrinsic and imperfection spin resonances add up coherently near the super strong resonances beyond 120 GeV, but mostly cancel out and result in generally weak resonance strengths at lower beam energies. Detailed simulations confirm that beam polarization can be mostly maintained in the fast acceleration to 45.6 GeV and 80 GeV, but severe depolarization may occur at even higher energies. This study suggests the possibility of acceleration of polarized electron~(positron) beams to ultra-high beam energies without the help of Siberian snakes, and supports injecting highly polarized beams into the collider rings as an attractive solution for resonant depolarization measurements and longitudinal polarized colliding beam experiments for future 100~km scale circular e$^{+}$e$^{-}$ colliders.

Using betatron coupling to suppress horizontal intrinsic spin resonances driven by partial snakes

A method for using betatron coupling to suppress partial snake driven resonances in a synchrotron is described. While the partial snakes permit avoidance of the strong resonances associated with the vertical betatron motion of the particles, they also excite numerous weak resonances associated with the horizontal betatron motion. These resonances occur whenever the fractional spin tune equals the fractional horizontal betatron tune. Since these are the same frequencies at which depolarizing resonances from betatron coupling occur, coupling resonances can be intentionally driven to exactly cancel the resonance driving terms of the partial snakes, thereby avoiding polarization loss due to these resonance crossings. Presented here is an explicit derivation of the partial snake driven resonances as betatron sidebands of strong imperfection resonances and a description of a practical scheme for their correction using the Brookhaven AGS as an example. Tracking results that verify the suppression via coupling are presented.

Magnetic field tuning of spin resonance in TmFeO3 single crystal probed with THz transient

TmFeO3, a canted antiferromagnet, has two intrinsic spin resonance modes in the terahertz (THz) frequency regime: quasi-ferromagnetic (q-FM) mode and quasi-antiferromagnetic (q-AFM) mode. Both the q-FM and q-AFM modes show strong magnetic field and temperature dependence. Hereby, by employing THz time-domain spectroscopy combined with external magnetic field and low temperature system, we systematically investigated the magnetic field induced frequency shift of q-FM and q-AFM modes as well as the temperature driven spin reorientation phase transition in TmFeO3 single crystal. In contrast to the isotropic temperature dependent two-mode, the magnetic field dependence of two-mode is strongly anisotropic: the magnetic field applied along c-axis (a-axis) can harden (soften) the spin resonance frequency of q-FM mode for Γ4 phase of TmFeO3, and the field applied along b-axis shows negligible frequency shift for the q-FM mode, with the q-AFM mode relatively stable. The present study provides solid evidence that the magnetic anisotropy in rare earth orthoferrite plays a dominant role in the q-FM mode and the occurrence of spin reorientation phase transition. With the magnetic anisotropic energy obtained from the temperature dependent q-FM and q-AFM mode frequencies, we can predict both magnetic field and temperature dependence of spin resonance in TmFeO3 single crystal via phenomenological analysis.

Intrinsic spin resonance in iron pnictides

Intrinsic spin resonance in iron pnictides

Acceleration of Polarized Protons up to 3.4 GeV/c in the Nuclotron at JINR

To preserve proton polarization in the Nuclotron up to 13.5 GeV/c, it is enough to use a partial solenoid snake with maximal field integral of 25 Tm that allows one to eliminate crossings of the most dangerous intrinsic and integer spin resonances. The insertion of weak field integral is sufficient to preserve the proton polarization up to 3.4 GeV/c. This momentum corresponds to the first intrinsic resonance. To preserve polarization during crossings of five integer spin resonances, it is possible to choose crossing rates that correspond to either the fast or the slow resonance crossings. Another possibility is a deliberate increasing of the resonance strength. To eliminate depolarization during protons injection into the Nuclotron, a scheme of matching of the polarization with a vertical direction is presented. During the run in February-March 2017, the three measurements of the proton polarization at kinetic energies of 0.5 GeV, 1 GeV and 2 GeV were made that allow one to obtain the integer spin resonances strengths.

Effect of Overlapping Intrinsic Spin Resonances on e-Lens Lattices from FY13 Polarized Proton Run

During the 2013 Polarized Proton run RHIC was run with a lattice designed to accommodate the phases necessary for the Electron lens. This lattice resulted in significant changes in magnitude and distribution of the intrinsic resonances. The overall magnitude of the strong intrinsic resonances were smaller, however the neighbouring weak intrinsic resonances grew. We present results from 2D direct tracking with 5,000 particles and 2D lattice independent tracking .

Entanglement of spin-orbit qubits induced by Coulomb interaction

Spin-orbit qubit (SOQ) is the dressed spin by the orbital degree of freedom through a strong spin-orbit coupling. We show that Coulomb interaction between two electrons in quantum dots located separately in two nanowires can efficiently induce quantum entanglement between two SOQs. The physical mechanism to achieve such quantum entanglement is based on the feasibility of the SOQ responding to the external electric field via an intrinsic electric dipole spin resonance.

BNL alternating gradient synchrotron with four helical magnets to minimize the losses of the polarized proton beam

The principle of using multiple partial helical magnets to preserve the polarization of the proton beam during its acceleration was applied successfully to the alternating gradient synchrotron (AGS) which currently operates with two partial helical magnets. In this paper we further explore this idea by using four partial helical magnets placed symmetrically in the AGS ring. This provides many advantages over the present setup of the AGS, which uses two partial helical magnets. First, the symmetric placement of the four helical magnets and their relatively lower field of operation allows for better control of the AGS optics with reduced values of the beta functions especially near beam injection and allows both the vertical and horizontal tunes to be placed within the ``spin tune gap,'' therefore eliminating the horizontal and vertical intrinsic spin resonances of the AGS during the acceleration cycle. Second, it provides a wider spin tune gap. Third, the vertical spin direction during beam injection and extraction is closer to vertical. Although the spin tune gap, which is created with four partial helices, can also be created with a single or two partial helices, the high field strength of a single helical magnet which is required to generate such a spin tune gap makes the use of the single helical magnet impractical, and that of the two helical magnets rather difficult. In this paper we will provide results on the spin tune and on the optics of the AGS with four partial helical magnets, and compare them with those from the present setup of the AGS that uses two partial helical magnets. Although in this paper we specifically discuss the effect of the four partial helices on the AGS, this method which can eliminate simultaneously the vertical and horizontal intrinsic spin resonances is a general method and can be applied to any medium energy synchrotron which operates in similar energy range like the AGS and provides the required space to accommodate the four helices. In addition, the four partial helix solution is an optimum solution because it eliminates all the spin resonances for any synchrotron which operates in the same energy range as the AGS.

Observation of snake resonances at Relativistic Heavy Ion Collider

The Siberian snakes are powerful tools in preserving polarization in high energy accelerators has been demonstrated at the Brookhaven Relativistic Heavy Ion Collider (RHIC). Equipped with two full Siberian snakes in each ring, polarization is preserved during acceleration from injection to 100 GeV. However, the Siberian snakes also introduce a new set of depolarization resonances, i.e. snake resonances as first discoverd by Lee and Tepikian [1]. The intrinsic spin resonances above 100 GeV are about a factor of two stronger than those below 100 GeV which raises the challenge to preserve the polarization up to 250 GeV. In 2009, polarized protons collided for the first time at the RHIC design store energy of 250 GeV. This paper presents the experimental measurements of snake resonances at RHIC. The plan for avoiding these resonanances is also presented.

Ferromagnetic microdisks as carriers for biomedical applications

We report the fabrication process, magnetic behavior, as well as the surface modification of ferromagnetic microdisks suspended in aqueous solution. They posses unique properties such as high magnetization of saturation, zero remanence due to spin vortex formation, intrinsic spin resonance at low frequencies, and the capability of delivering various biomolecules at once. Furthermore, because of their anisotropic shape, our magnetic particles rotate under alternating magnetic fields of small amplitude. This can be used to promote the idea of advanced therapies, which include combined drug delivery and magnetomechanical cell destruction when targeting tumor cells. The approach enables us to fabricate suitable magnetic carriers with excellent size tolerances, and then release them from the wafer into solution, ready for surface modification and therapeutic use. The particles have a magnetic core and are covered with few nanometers of gold on each side to provide stability at ambient conditions as well as biocompatibility and selective adhesion functions. A successful attempt to bind thiolates, including SH-modified antibody, to the disk’s surface was demonstrated.

Unexpected reduction of rf spin resonance strength for stored deuteron beams

Stored beams of polarized protons, electrons, or deuterons can be spin flipped by sweeping an rf dipole's or solenoid's frequency through an rf spin resonance. Fitting such data to the modified Froissart-Stora equation's spin resonance strength ${\mathcal{E}}_{\mathrm{FS}}$ gave very large deviations from the $^{*}\mathcal{E}_{Bdl}$ obtained from each rf magnet's $\ensuremath{\int}{B}_{rms}dl$. We recently varied an rf dipole's frequency sweep range $\ensuremath{\Delta}f$, and the momentum spread $\ensuremath{\Delta}p/p$ and betatron tune ${\ensuremath{\nu}}_{y}$ of stored $1.85\text{ }\text{ }\mathrm{GeV}/c$ polarized deuterons. We found a sharp constructive interference when ${\ensuremath{\nu}}_{y}$ was near an intrinsic spin resonance. Moreover, over large $\ensuremath{\Delta}f$ and $\ensuremath{\Delta}p/p$ ranges, ${\mathcal{E}}_{\mathrm{FS}}$ was about 7 times smaller than the predicted $^{*}\mathcal{E}_{Bdl}$.

Exploration of horizontal intrinsic spin resonances with two partial Siberian snakes

Two partial Siberian snakes were used to avoid all the spin imperfection and vertical intrinsic resonances in the alternating gradient synchrotron (AGS) at Brookhaven National Laboratory. However, the horizontal betatron motion can cause polarization loss resulting from the nonvertical stable spin direction in the presence of two partial snakes. This type of resonance, called a horizontal intrinsic spin resonance, was observed and systematically studied in the AGS. A simplified analytic model and numerical simulation have been developed to compare with experimental data. Properties of the horizontal intrinsic resonance are discussed.

Unexpected enhancements and reductions of rf spin resonance strengths

We recently analyzed all available data on spin-flipping stored beams of polarized protons, electrons, and deuterons. Fitting the modified Froissart-Stora equation to the measured polarization data after crossing an rf-induced spin resonance, we found 10--20-fold deviations from the depolarizing resonance strength equations used for many years. The polarization was typically manipulated by linearly sweeping the frequency of an rf dipole or rf solenoid through an rf-induced spin resonance; spin-flip efficiencies of up to $99.9%$ were obtained. The Lorentz invariance of an rf dipole's transverse $\ensuremath{\int}Bdl$ and the weak energy dependence of its spin resonance strength $\mathcal{E}$ together imply that even a small rf dipole should allow efficient spin flipping in 100 GeV or even TeV storage rings; thus, it is important to understand these large deviations. Therefore, we recently studied the resonance strength deviations experimentally by varying the size and vertical betatron tune of a $2.1\text{ }\text{ }\mathrm{GeV}/c$ polarized proton beam stored in COSY. We found no dependence of $\mathcal{E}$ on beam size, but we did find almost 100-fold enhancements when the rf spin resonance was near an intrinsic spin resonance.

Polarized Proton Collisions at 205 GeV at RHIC

The Brookhaven Relativistic Heavy Ion Collider (RHIC) has been providing collisions of polarized protons at a beam energy of 100 GeV since 2001. Equipped with two full Siberian snakes in each ring, polarization is preserved during acceleration from injection to 100 GeV. However, the intrinsic spin resonances beyond 100 GeV are about a factor of 2 stronger than those below 100 GeV making it important to examine the impact of these strong intrinsic spin resonances on polarization survival and the tolerance for vertical orbit distortions. Polarized protons were first accelerated to the record energy of 205 GeV in RHIC with a significant polarization measured at top energy in 2005. This Letter presents the results and discusses the sensitivity of the polarization survival to orbit distortions.

Quadrupole-mode transfer function and the nonlinear Mathieu instability.

We show that the quadrupole-mode transfer function (QTF) is a powerful nondestructive tool to measure properties of dynamical systems. In particular, we discuss the feasibility of using the QTF to measure the betatron tunes and the beam emittances with a beam-position monitor system. The QTF can also be used to compensate the optical mismatch during the beam injection process. However, it is less effective than the rf dipole method in overcoming the intrinsic spin resonances for polarized beam acceleration.

Observation of a hybrid spin resonance

A new type of spin depolarization resonance has been observed at the Brookhaven Alternating Gradient Synchrotron (AGS). This spin resonance is identified as a strong closed-orbit sideband around the dominant intrinsic spin resonance. The strength of the resonance was proportional to the 9th harmonic component of the horizontal closed orbit and proportional to the vertical betatron oscillation amplitude. This "hybrid" spin resonance cannot be overcome by the partial snake at the AGS, but it can be corrected by the harmonic orbit correctors.

Overcoming Intrinsic Spin Resonances with an rf Dipole

A coherent spin resonance excited by an rf dipole was used to overcome depolarization due to intrinsic spin resonances at the Alternating Gradient Synchrotron (AGS) at Brookhaven National Laboratory. We found that our data are consistent with a full spin flip of a polarized proton beam, without emittance growth, at G{gamma}=12+{nu}{sub z} and 36{minus}{nu}{sub z} , by adiabatically exciting a vertical coherent betatron oscillation using a single rf dipole magnet. The interference pattern observed between the intrinsic spin resonance and the coherent spin resonance agrees well with multiparticle spin simulations based on a simple two-resonance model. The interference pattern can be used for beam diagnostics. {copyright} {ital 1998} {ital The American Physical Society}

Interactions of α-Lactalbumin with Fatty Acids and Spin Label Analogs

Bovine alpha-lactalbumin (alpha-LA) has been shown by intrinsic protein fluorescence and electron spin resonance methods to interact with the spin-labeled fatty acid analog, 5-doxylstearic acid, as well as stearic acid. An intrinsic fluorescence titration of various alpha-LA forms with 5-doxylstearic acid causes first an increase and then a decrease in emission intensity with concomitant shifts in tryptophan emission wavelength. In some cases, up to three steps in the fluorescence titration curves were visible, which were fit to apparent binding steps from 10(-6) to 10(-4) M. The binding parameters of 5-doxylstearic acid for apo- and Ca2+-alpha-LA were an order of magnitude different from one another; the stronger one, apo-alpha-lactalbumin, exhibited a Kd of 35 microM. Electron spin resonance titrations of 5-doxylstearic acid-loaded apo-alpha-LA with stearate (micelles) seem to suggest separate binding loci if alpha-LA indeed binds stearate at these concentrations. The titration of alpha-LA by stearic acid results in a fluorescence emission red shift and an apparent stepped increase in fluorescence intensity. Lipid-protein association occurred at concentrations at which stearic acid micelles and aggregates begin to form in the absence of protein. Nonetheless, the relatively strong association between stearic acid and apo-alpha-LA was also confirmed by means of the fluorescent indicator acrylodated fatty acid binding protein, in which addition of alpha-LA to the stearate-loaded indicator protein reverses the decrease in fluorescence of the acrylodan chromophore conjugated to the protein.

Self-polarization of protons in storage rings

It has been proposed that stored proton or heavy ion beams can be polarized by spatially separating particles with opposite spin directions, using the Stern-Gerlach effect in alternating quadrupole fields. The growth rate of the vertival betatron amplitude is calculated for beam halves with opposite polarizations rotating in the horizontal plane, at intrinsic spin resonance a γ ± ν y = integer. This polarization method would work best with rings having large diameter, low vertical emittance, low vertical betatron tune, and strong superconducting quadrupoles. Provided that suitable strong quadrupoles exist, the method might advantageously replace the present technique for obtaining polarized proton or heavy ion beams, where low energy polarized beams are first generated by a source and then accelerated through numerous depolarizing resonances up to the final energy. Although the proposed self-polarization in the present colliders and storage rings might be impractically slow, it is shown that in a purpose-built machine the vertical splitting rate of the beam might be reasonably fast compared with the beam blowup or decay.