Based on the potential theory and perturbation techniques, the problem of second-order sloshing in a three-dimensional tank in combination with surge and sway motions is analyzed. When excitation is applied in both ho...Based on the potential theory and perturbation techniques, the problem of second-order sloshing in a three-dimensional tank in combination with surge and sway motions is analyzed. When excitation is applied in both horizontal directions, the second-order resonance can occur when the sum frequency or the difference frequency of any two excitation components is equal to one of the natural frequencies. The resonance can also occur when the sum or difference frequency of one of the excitation frequencies and one of the natural frequencies is equal to another natural frequency.展开更多
The betatron matching of a rotationally asymmetric beam in space charge dominated low-energy beam transports （LEBTs） where solenoids are used for the transverse matching has been studied. For better understanding, t...The betatron matching of a rotationally asymmetric beam in space charge dominated low-energy beam transports （LEBTs） where solenoids are used for the transverse matching has been studied. For better understanding, the coupling elements of a beam matrix are interpreted in special forms that are products of a term defined by the Larmor rotation angle and another by the difference between the beam matrix elements in the two transverse planes. The coupling form originally derived from the rotationally symmetric field in solenoids still holds when taking into account the rotationally asymmetric space charge forces that are due to the unequal emittance in the two transverse planes. It is shown in this paper that when an LEBT mainly comprising solenoids transports a beam having unequal emittance in the two transverse planes and the linear space charge force is taken into account, the initial Twiss parameters can be modified to obtain the minimum and equal emittance at the LEBT exit. The TRACE3D calculations also prove the principle. However, when quadrupoles that are also rotationally asymmetric are involved in between solenoids, the coupling between the two transverse planes becomes more complicated and the emittance increase is usually unavoidable. A matching example using the CSNS （China Spallation Neutron Source） LEBT conditions is also presented.展开更多
基金supported by the National Science Foundation of China(Grant No.51079082)
文摘Based on the potential theory and perturbation techniques, the problem of second-order sloshing in a three-dimensional tank in combination with surge and sway motions is analyzed. When excitation is applied in both horizontal directions, the second-order resonance can occur when the sum frequency or the difference frequency of any two excitation components is equal to one of the natural frequencies. The resonance can also occur when the sum or difference frequency of one of the excitation frequencies and one of the natural frequencies is equal to another natural frequency.
基金Supported by CAS Knowledge Innovation Program-'CSNS R&D Studies'National Natural Science Foundation of China(10775153)
文摘The betatron matching of a rotationally asymmetric beam in space charge dominated low-energy beam transports （LEBTs） where solenoids are used for the transverse matching has been studied. For better understanding, the coupling elements of a beam matrix are interpreted in special forms that are products of a term defined by the Larmor rotation angle and another by the difference between the beam matrix elements in the two transverse planes. The coupling form originally derived from the rotationally symmetric field in solenoids still holds when taking into account the rotationally asymmetric space charge forces that are due to the unequal emittance in the two transverse planes. It is shown in this paper that when an LEBT mainly comprising solenoids transports a beam having unequal emittance in the two transverse planes and the linear space charge force is taken into account, the initial Twiss parameters can be modified to obtain the minimum and equal emittance at the LEBT exit. The TRACE3D calculations also prove the principle. However, when quadrupoles that are also rotationally asymmetric are involved in between solenoids, the coupling between the two transverse planes becomes more complicated and the emittance increase is usually unavoidable. A matching example using the CSNS （China Spallation Neutron Source） LEBT conditions is also presented.
