CN114641121B - Method for tuning field stability - Google Patents

Method for tuning field stability Download PDF

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CN114641121B
CN114641121B CN202210287286.0A CN202210287286A CN114641121B CN 114641121 B CN114641121 B CN 114641121B CN 202210287286 A CN202210287286 A CN 202210287286A CN 114641121 B CN114641121 B CN 114641121B
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rod coupler
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insertion depth
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于旭东
雷钰
邢庆子
郑曙昕
马鹏飞
王帅
王学武
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Tsinghua University
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Abstract

The invention relates to a field stability tuning method of an Alvarez type drift tube linear accelerator, wherein each acceleration gap of the Alvarez type drift tube linear accelerator forms an acceleration unit respectively, and the method comprises the following steps: step S1: the method comprises the steps that a transmission line model is built for the Alvarez type drift tube linear accelerator, the structures of a drift tube, a support rod and a rod coupler are equivalent to impedance parameters in a transmission line equivalent circuit by the transmission line model, and the working mode frequency of a linear accelerator cavity and the electric field distribution of each accelerating unit can be obtained according to the insertion depth of each rod coupler; step S2: and inserting the rod coupler into a cavity of the linear accelerator, continuously measuring the inclination sensitivity of the cavity, and adjusting the insertion depth of the rod coupler according to an iterative calculation result which is carried out from the current insertion depth of the rod coupler to the direction with the minimum inclination sensitivity based on the constructed transmission line model until the insertion depth of each rod coupler is obtained when the inclination sensitivity meets the requirement.

Description

Method for tuning field stability
Technical Field
The invention relates to a field stability tuning method, in particular to a field stability tuning method for an Alvarez (Alvarez) drift tube linear accelerator (DTL).
Background
The Alvarez type drift tube linear accelerator can accelerate low-energy proton beams or heavy ion beams, and is one of the low-energy linear accelerators commonly used in the field of proton heavy ion accelerators. Alvarez-type drift tube linear accelerators are usually connected to a Radio Frequency Quadrupole (RFQ) accelerator to further accelerate the proton heavy ion beam, and are commonly used in synchrotron implanters.
The alvarez-type drift tube linear accelerator is configured by arranging two or more drift tube electrodes in a hollow cylindrical shape along the beam traveling direction in a cylindrical resonant cavity, as shown in fig. 1. High-frequency power is provided in the cylindrical resonant cavity, and proton heavy ions are accelerated along the advancing direction of the beam by a high-frequency electric field generated between the drift tube electrodes. The arrangement of the drift tube electrodes is designed such that charged particles are present within the drift tube electrodes when the high frequency electric field is directed opposite to the direction of beam travel. The acceleration gaps between each drift tube electrode and the half drift tubes on the two sides respectively form an acceleration unit.
The resonant cavity working mode of the Alvarez type drift tube linear accelerator is a Transverse Magnetic (TM) mode, and due to the particularity of a radio frequency structure, the Alvarez type drift tube linear accelerator has the characteristic of unstable field distribution, namely the field distribution of the cavity is sensitive to the change of the internal dimension of the cavity, and other resonant modes close to the frequency are easily excited. At present, the mainstream international method for improving the field stability is to introduce a rod coupler structure into a cavity of a drift tube linear accelerator. Since alvarez drift tube linear accelerators usually contain a large number of rod couplers and the interaction effects between the rod couplers affect each other, it is necessary to rely on a field stability tuning method for field stability tuning. As shown in fig. 2. The field stability tuning is realized by adjusting the insertion depth of the rod coupler in the cavity (i.e. changing the distance between the rod coupler and the drift tube) in the cold measurement tuning process of the cavity.
The working mode of the resonant cavity of the alvarez type drift tube linear accelerator is a TM010 mode in transverse magnetic modes, actually, other transverse magnetic modes can exist in the resonant cavity of the alvarez type drift tube linear accelerator, and the transverse magnetic mode adjacent to the working mode is a transverse magnetic mode (TM 011) mode adjacent to the working mode. The rod coupler (PC) mode is formed by resonance between the rod couplers after the rod couplers are inserted into the cavity, wherein the highest frequency mode of all the rod coupler (PC) modes is the highest rod coupler mode (PC 01).
Currently, the tilt sensitivity is used as a characterization index of the field stability of the alvarez drift tube linear accelerator, and the measurement mode of the tilt sensitivity is as follows: measuring the voltage distribution V of each acceleration unit 1 In the Alvarez typeRespectively introducing frequency perturbation delta f and-delta f into the inlet end and the outlet end of the drift tube linear accelerator, and then measuring the voltage distribution V of each accelerating unit after perturbation 2 Then, the tilt sensitivity is calculated by the following equation:
T＝(V 2 -V 1 )/(δfV 1 )。 (1)
wherein a higher tilt sensitivity indicates a lower field stability.
The tuning method for the field stability of the mainstream alvarez type drift tube linear accelerator in the world is a trial and error method. As the name suggests, the trial-and-error method needs to artificially summarize the relationship between the rod coupler and the field stability in the tuning process, estimate the insertion depth according to the current field stability of each accelerating unit and the action trend of the rod coupler on the field stability, and need the tuning personnel to trial and error repeatedly in the tuning process until the field stability meets the index requirement. For alvarez-type drift tube linear accelerators with a large number of rod couplers, the trial-and-error method can increase the working time and workload of the tuner linearly.
Disclosure of Invention
In order to solve the above technical problem, the present invention provides a method for tuning field stability of an alvarez drift tube linear accelerator, wherein each acceleration gap of the alvarez drift tube linear accelerator constitutes one acceleration unit, the method comprising: step S1: a transmission line model is constructed for the Alvarez type drift tube linear accelerator, the transmission line model enables the structures of the drift tube, the supporting rod and the rod coupler to be equivalent to impedance parameters in an equivalent circuit of the transmission line, and the working mode (TM 010) frequency (f) of a linear accelerator cavity can be obtained according to the insertion depth of each rod coupler 0 ) And an electric field distribution (V) of each accelerating element; step S2: and inserting the rod coupler into the cavity of the linear accelerator, continuously measuring the inclination sensitivity of the cavity, and adjusting the insertion depth of the rod coupler according to the iterative calculation result of the constructed transmission line model from the current insertion depth of the rod coupler to the direction with the minimum inclination sensitivity until the insertion depth of each rod coupler is obtained when the inclination sensitivity meets the requirement.
Preferably, in the above-described step S1 of constructing the transmission line model, the frequency f is determined according to the operation mode in a state where the rod coupler is not inserted for the cavity of the linac 0 And determining the local frequency f of each accelerating unit of the linear accelerator according to the measurement result of the voltage distribution of each accelerating unit 0 The equivalent inductance of the supporting rod is determined according to the measurement result of the frequency of the adjacent transverse magnetic modes of the working mode under the condition that the rod coupler is not inserted into the cavity of the linear accelerator, the equivalent inductance of the rod coupler is determined according to the mode frequency of the highest rod coupler and the voltage distribution measurement result of each accelerating unit under the condition that the rod coupler is inserted into the cavity of the linear accelerator in the equal depth, and the relation curve between the insertion depth of the rod coupler and the mode frequency of the highest rod coupler is determined according to the measurement result of the mode frequency of the highest rod coupler under the condition that the rod coupler is inserted into the cavity of the linear accelerator in the equal depth.
The objective of the field stability tuning method according to the invention is to adjust the insertion depth of each rod coupler such that the tilt sensitivity of the cavity is satisfactory. The above steps provide a method for constructing a transmission line model, and then performing iterative computation based on the transmission line model to indicate how to adjust the insertion depth of the rod coupler. The impedance parameters in the transmission line model mainly include equivalent inductance of the drift tube, capacitance between the drift tube and the cavity wall, capacitance between the drift tubes, equivalent inductance of the support rod, equivalent inductance of the rod coupler, and capacitance between the rod coupler and the drift tube, wherein the local frequency f of each acceleration unit determined in the step S1 0n The equivalent inductance of the drift tube and the capacitance between the drift tube and the cavity wall are reflected; the capacitance between the drift tube and the cavity wall and the capacitance between the drift tubes are known per se for a given accelerator cavity and drift tube; the equivalent inductance of the supporting rod and the equivalent inductance of the rod coupler are determined in the step S1; the capacitance between the rod coupler and the drift tube (corresponding to the rod coupler frequency) is determined by the rod coupler insertion depth. Therefore, the transmission line model constructed by the steps actually defines the mapping relation between the insertion depth of the rod coupler and the working mode frequency of the cavity of the linear accelerator, and can be coupled by the rodThe insertion depth of the linear accelerator cavity is used as an input variable to solve the working mode frequency of the linear accelerator cavity and the electric field distribution of each accelerating unit. Thus, the corresponding tilt sensitivity can be calculated by introducing frequency perturbations. Under the condition that the inclination sensitivity can be calculated from the insertion depth of the rod coupler based on the constructed transmission line model, the required inclination sensitivity can be obtained by continuously measuring and adjusting the insertion depth of the rod coupler through an iterative calculation method, so that the insertion depth of each rod coupler corresponding to the finally obtained inclination sensitivity can be used as the final tuning result of the field stability tuning method. Since the process uses iterative calculations of a single control variable (rod coupler insertion depth) with tilt sensitivity as a control condition, and the calculated and measured values are continuously compared, it is independent of operator experience and can be used to more quickly and accurately trend the final tuning result in the case of multiple rods, compared to the methods of trial-and-error adjustment of tilt sensitivity, which are now commonly used in the art.
According to a preferred embodiment of the tuning method of field stability according to the present invention, the above step S1 for constructing a transmission line model for the alvarez drift tube linear accelerator comprises:
step S11: measuring the frequency (f) of the working mode (TM 010) of a linear accelerator without a rod coupler inserted in the cavity 0 ) Taking the measured values as the local frequencies (f) of all accelerating elements in the transmission line model 0n )；
Step S12: according to the length L of the accelerating unit i Constructing a transmission line model for a non-strut rod and rod coupler and working mode (TM 010) frequency (f) based on the transmission line model 0 ) Local frequencies (f) of nearby sets of accelerating units 0n ) Calculating voltage distribution calculation values of a plurality of groups of accelerating units;
step S13: measuring the actual voltage distribution of each accelerating unit of the linear accelerator in the state that the rod coupler is not inserted into the cavity to obtain the voltage distribution measured value of each accelerating unit, and dividing the voltage of each accelerating unit closest to the measured voltage distribution measured value of each accelerating unitThe local frequency of each acceleration unit corresponding to the calculated value is determined as the local frequency (f) of each new acceleration unit 0n )；
Step S14: the local frequency of each acceleration unit in the transmission line model is replaced with the new local frequency (f) of each acceleration unit determined in step S13 0n )；
Step S15: measuring the frequency of a working mode adjacent transverse magnetic mode (TM 011) of a linear accelerator cavity in a state of not inserting a rod coupler to obtain a frequency measurement value of the TM011 frequency;
step S16: adding equivalent inductance L of support rod in transmission line model s /l 0 Selecting a plurality of supporting rod equivalent inductance theoretical values according to a preset supporting rod equivalent inductance step length in a preset range above and below a supporting rod equivalent inductance theoretical value determined based on the geometric dimensions of the supporting rod and the drift tube, calculating TM011 frequency based on the supporting rod equivalent inductance theoretical values to obtain a plurality of TM011 frequency calculated values, and taking the supporting rod equivalent inductance theoretical value corresponding to the TM011 frequency calculated value closest to the TM011 frequency measured value measured in the step S15 as the supporting rod equivalent inductance of the transmission line model;
step S17: inserting each rod coupler in the cavity of the linear accelerator in a medium depth manner, measuring the mode (PC 01) frequency of the highest rod coupler of the linear accelerator and the voltage distribution of each accelerating unit, and obtaining the measured value of the mode frequency of the highest rod coupler and the voltage distribution measured value of each accelerating unit;
step S18: adding equivalent inductance of rod coupler in transmission line model, and converting the frequency f of each rod coupler in the transmission line model pn Setting the measured value of the highest rod coupler mode (PC 01) frequency, selecting a plurality of rod coupler equivalent inductance theoretical values according to a preset rod coupler equivalent inductance step length in a preset range above and below a rod coupler equivalent inductance theoretical value determined based on the geometric dimension of the rod coupler, calculating the voltage distribution of each accelerating unit based on the rod coupler equivalent inductance theoretical values to obtain a plurality of groups of voltage distribution calculated values of each accelerating unit, and calculating the voltage distribution calculated value closest to the voltage distribution measured value of each accelerating unit measured in the step S17The corresponding rod coupler equivalent inductance is used as the rod coupler equivalent inductance of the transmission line model;
step S19: the method comprises the steps of inserting rod couplers with different insertion depths into a cavity of the linear accelerator, measuring a variation curve of the highest rod coupler mode (PC 01) frequency after the rod couplers are inserted into the cavity of the linear accelerator with the same insertion depth, fitting the curve, and replacing the highest rod coupler mode frequency in a transmission line model with the insertion depth of the rod couplers according to the fitted curve.
In the above steps S11 to S14, different local frequency values are taken near the initial value of the local frequency given to each acceleration unit to obtain the local frequency combinations of several groups of acceleration units, and then the voltage distribution of each acceleration unit corresponding to the local frequency of each group of acceleration units is calculated, and the local frequency of each acceleration unit of the group closest to the actually measured voltage distribution measurement value of each acceleration unit is taken as the local frequency of each acceleration unit. The frequency of the working mode (TM 010) of the cavity of the linear accelerator measured in the step S11 is not substantially affected by the equivalent inductance of the supporting rod in the transmission line model. Therefore, the measured values do not reflect the influence of the equivalent inductance of the supporting rod when the local frequency of each acceleration unit is calculated as described above, and therefore, the influence of the supporting rod and the rod coupler which is not inserted yet can be eliminated when each parameter of the transmission line model is solved, so that the local frequency of each acceleration unit can be determined through the above method steps.
The reason why the operation mode adjacent transverse magnetic mode (TM 011) frequency of the linear accelerator cavity in the state where the rod coupler is not inserted is measured in the above step S15, not the operation mode (TM 010) frequency, is that the TM011 frequency is greatly affected by the equivalent inductance of the supporting rod in the transmission line model, whereas the TM010 frequency is not substantially affected by the equivalent inductance of the supporting rod in the transmission line model as described above. Therefore, the calculation using the frequency of the working mode adjacent transverse magnetic mode (TM 011) in steps S15 and S16 means that after the local frequency of each accelerating unit in the transmission line model is obtained, the equivalent inductance of the strut can be calculated based on the influence of the equivalent inductance of the strut on the frequency of the working mode adjacent transverse magnetic mode (TM 011). When the equivalent inductance of the supporting rod and the local frequency of each accelerating unit are determined, the rod coupler can be inserted into the cavity in step S17 and step S18, that is, the influence of the insertion depth of the rod coupler on the transmission line model can be considered separately at this time, and the transmission line model can be further corrected. Specifically, in step S17 of inserting each rod coupler at equal depth, the measured value of the highest rod coupler mode (PC 01) frequency for comparison with the theoretical equivalent inductance values of several sets of rod couplers in step S18 can be obtained by just inserting each rod coupler at equal depth into the linear accelerator cavity once. Here, the theoretical equivalent inductance value of the rod coupler is determined based on the geometric dimensions of the rod coupler.
According to a preferred embodiment of the field stability tuning method of the present invention, in the above step S13 for re-determining the local frequency of each acceleration unit, a voltage distribution calculation value of each acceleration unit closest to the measured voltage distribution measurement value of each acceleration unit is determined based on a genetic algorithm or an intrinsic perturbation method from among the sets of voltage distribution calculation values of each acceleration unit calculated in the above step S12.
According to a preferred embodiment of the tuning method for field stability of the present invention, the step S2 of solving the insertion depth of each rod coupler through iterative computation based on the constructed transmission line model comprises:
step S21: inserting the rod couplers into a cavity of the linear accelerator, recording the initial insertion depth of each rod coupler, and measuring the inclination sensitivity of the cavity to obtain the current measurement value of the inclination sensitivity;
step S22: calculating tilt sensitivities corresponding to all possible combinations of the insertion depths of the rod couplers selected according to a preset step length in a preset range above and below the current insertion depth of each rod coupler according to the transmission line model determined in the step S1, and determining the insertion depth l of each rod coupler corresponding to the minimum tilt sensitivity s,n ；
Step S23: calculating the current insertion depth of each rod coupler within the preset range from top to bottom according to the transmission line model determined in the step S1The inclination sensitivity corresponding to all possible combinations of the insertion depths of the rod couplers selected by the preset step length is determined, and the insertion depth l of each rod coupler corresponding to the inclination sensitivity closest to the current measurement value of the inclination sensitivity is determined e,n ；
Step S24: the insertion depth l of each rod coupler corresponding to the minimum tilt sensitivity determined in step S22 s,n The insertion depth l of each rod coupler corresponding to the tilt sensitivity determined in step S23 which is closest to the current measurement value of tilt sensitivity e,n Difference Δ l between n Adjusting the insertion depth of each rod coupler as an adjustment quantity, and then measuring the cavity tilt sensitivity to obtain the current measurement value of the tilt sensitivity;
step S25: and judging whether the current measurement value of the tilt sensitivity meets the requirement, if so, ending the adjustment of the insertion depth of each rod coupler, and if not, repeating the arrangement from step S22 or S23 to step S25 based on the current insertion depth of each rod coupler.
It should be understood that, in the iterative calculation process defined by steps S21 to S25, all possible combinations of insertion depths of the rod couplers selected by predetermined steps within predetermined ranges above and below the current insertion depth of the rod couplers first calculated by step S22 based on the constructed transmission line model may be always adopted, which means that all possible combinations of insertion depths of the rod couplers are selected within the spans of predetermined ranges above and below the initial depth of the rod coupler into the cavity of the linear accelerator, and remain unchanged after being calculated, and in the subsequent iterative calculation, it is only necessary to return to step S23 from step S25 if necessary, and the tilt sensitivities of the possible combinations are directly calculated in step S23; obviously, it is also conceivable that, returning to step S22 each time when returning from step S25, all possible combinations of insertion depths of the rod couplers are selected according to the current insertion depths of the rod couplers within a span of a predetermined range above and below the current insertion depth of the rod couplers, which may not completely coincide with all possible combinations when step S22 was performed last time because the current insertion depths of the rod couplers have changed after step S22 was performed last time. In contrast, the solution of returning to step S22 provides a faster iterative computation speed.
According to a preferred embodiment of the field stability tuning method of the present invention, in the above step S21 of inserting the rod couplers into the cavity of the linear accelerator and recording the initial insertion depth of each rod coupler, all rod couplers are inserted at the same initial insertion depth by equal depth. According to the coupled cavity chain theory, when a TM01n mode dispersion curve and a rod coupler mode (PC) dispersion curve are merged, the cavity tilt sensitivity can be obviously changed, and a TM010 frequency point is located between the highest rod coupler mode (PC 01) frequency point and an adjacent transverse magnetic mode (TM 011) frequency point of a working mode and approximately located at the center of the distance between the highest rod coupler mode (PC 01) frequency point and the adjacent transverse magnetic mode (TM 011) frequency point of the working mode. Therefore, it is more preferable that, in the above step S21, the initial insertion depth is set such that the PC01 frequency measurement value in the cavity is 2 times the TM010 frequency measurement value and the TM011 frequency measurement value.
Preferably, in the step S22, only the tilt sensitivities corresponding to combinations of insertion depths not calculated among all possible combinations of insertion depths of the rod couplers selected by a predetermined step in a predetermined range above and below the current insertion depth of the rod couplers are calculated and compared with the current minimum tilt sensitivity to determine a new minimum tilt sensitivity. That is, if the span size of the predetermined range above and below the current insertion depth of the rod coupler remains unchanged, and if the iterative calculation process returns to step S22 after steps S23 to S25, the predetermined range above and below the current insertion depth of the rod coupler includes a part of the previously-recalculated combination of insertion depths due to a change in the current insertion depth of the rod coupler relative to the previous execution of step S22. In this case, the portion of the increment may be calculated.
In the above step S25 of determining whether the tilt sensitivity current measurement value meets the requirement, the requirement for the tilt sensitivity current measurement value is that the tilt sensitivity current measurement value is less than or equal to a (preset) tilt sensitivity target value. If the current measured value of the tilt sensitivity is less than the target value of the tilt sensitivity, it is determined that the target value of the tilt sensitivity is satisfactory, and the iterative calculation is not continued, and the current insertion depth of each rod coupler is used as the final result of the field stability tuning method according to the present invention. However, alternatively or additionally, the decrease of the tilt sensitivity current measurement value in the iteration process may be used as a judgment criterion, and if the decrease of the tilt sensitivity current measurement value with respect to the tilt sensitivity current measurement value before the adjustment of the insertion depth of each rod coupler is performed in step S24 is smaller than a predetermined decrease, it is judged that the tilt sensitivity current measurement value is satisfactory, and it is not necessary to continue the iteration.
Drawings
Embodiments of the present invention are explained below with reference to the drawings. In the drawings:
figure 1 schematically shows a cross-sectional view and an axial cross-sectional view of an alvarez drift tube linear accelerator;
fig. 2 schematically shows a part of a transmission line model of an alvarez-type drift tube linear accelerator;
figure 3 schematically shows the flow steps of a preferred embodiment of a field stability tuning method for an alvarez drift tube linear accelerator according to the invention.
Detailed Description
Figure 1 shows schematically in cross-section and longitudinal section the structure of a typical alvarez drift tube linear accelerator, with a series of drift tubes 10 supported by support rods 40 in the cavity, with gaps between the drift tubes and the walls of the acceleration cavity, and with a number of rod couplers 50 radially inserted inside the cavity for tuning the accelerator electric field. The field stability tuning method of the invention is based on the transmission line model of the Alwatts column type drift tube linear accelerator, the drift tube 10, the gap 30 between the drift tube and the accelerating cavity wall 20, the supporting rod 40, the rod coupler 50, the gap 60 between the rod coupler and the drift tube and other structures are equivalent to impedance parameters in an equivalent circuit, and then based on the transmission line model, the calculation of the voltage field distribution and the inclination sensitivity of the accelerating unit of the Alwatts column type drift tube linear accelerator is realized, thereby realizing the quantitative calculation of the insertion depth of the rod coupler.
When the transmission line model is solved, the drift tube and the inner wall of the cavity of the alvarez type drift tube linear accelerator are of a coaxial linear special structure, and the voltage field distribution can be solved by only the length of each accelerating unit, the local frequency of each accelerating unit, the equivalent inductance of the supporting rod, the equivalent inductance of the rod coupler and the frequency of the rod coupler, wherein the length of each accelerating unit can be obtained from a design and processing file of the drift tube linear accelerator, and when the supporting rod and the rod coupler are not considered in the transmission line model, the transmission line model is called a transmission line model without the supporting rod and the rod coupler.
FIG. 2 schematically shows a part of a transmission line model of an Alvarez drift tube linear accelerator, typically using measured local frequencies f of the respective accelerating elements 0n It is solved. As shown in fig. 2, 1 is the inductance per unit length of the drift tube, and 2 is the capacitance between the drift tube per unit length and the chamber wall. For the Alvarez type drift tube linear accelerator with N accelerating units, the whole transmission line model is divided into 2N sections by a capacitor 3 between drift tubes, a supporting rod equivalent inductor 4, a rod coupler equivalent inductor 5 and a capacitor 6 between the rod coupler and the drift tube, wherein the 2N-1 section is connected with the 2N section through the capacitor 3 between the drift tubes, and the 2N section is connected with the 2n +1 section through the supporting rod equivalent inductor 4 and the rod coupler equivalent inductor 5 and the capacitor 6 between the rod coupler and the drift tube. The potential of the ith section of the drift tube of the transmission line model satisfies
Figure BDA0003558784040000091
Wherein A is i And B i The coefficient of the ith section of the transmission line model is defined, f is the transverse magnetic mode frequency to be solved by the transmission line model, c is the speed of light in vacuum, and z is the cumulative length of the drift tube comprising the ith section. Hereinafter, the followingIn, memory
Figure BDA0003558784040000092
Is eta i ，
Figure BDA0003558784040000093
Is xi i ，η i And xi i The length L of each accelerating unit can be used i Performing calculation with the expression
Figure BDA0003558784040000094
When the model coefficient A of each transmission line is solved i And B i The transverse magnetic mode frequency f can obtain the voltage of each accelerating unit of the linear accelerator of the Alvarez drift tube, and the accelerating voltage U of the nth accelerating unit n The potential V of the drift tube can be measured from the front and the back of the acceleration unit 2n And V 2n-1 The difference is expressed as
U n ＝V 2n -V 2n-1 I.e. by
U n ＝(A 2n η 2n-1 +B 2n ξ 2n-1 )-(A 2n-1 η 2n-1 +B 2n-1 ξ 2n-1 ) I.e. by
U n ＝(A 2n -A 2n-1 )η 2n-1 +(B 2n -B 2n-1 )ξ 2n-1 (4)
Wherein the transverse magnetic mode frequency f can be solved by the following equation
Figure BDA0003558784040000101
Wherein M is k For a transmission line model matrix, when k =2n-1, M k Is expressed as
Figure BDA0003558784040000102
When k =2n, the number of the bits is set to k =2n,M k is expressed as
Figure BDA0003558784040000103
Wherein l 0 Inductance of drift tube per unit length, L p Is a rod coupler equivalent inductance, L s Equivalent inductance f of the support rod 0n For the nth acceleration unit local frequency, f pn For the nth rod coupler frequency, the expression is respectively
Figure BDA0003558784040000104
Figure BDA0003558784040000105
Wherein C is n Is the gap capacitance C between the drift tubes before and after the nth accelerating unit pn Is the capacitance between the nth rod coupler and the drift tube, L 2n-1 And L 2n Equivalent inductances of the drift tube before and after the nth accelerating unit are respectively.
As can be seen from the above expression, when the local frequency f of each acceleration unit on the transmission line model is determined 0n Each rod coupler frequency f pn 、l 0 /L p 、l 0 /L s The transverse magnetic mode frequency f can then be solved using equation (5) above. The equation has an infinite solution, where above f pn The first solution is the frequency of the working mode (TM 010) mode, and the second solution is the frequency of the working mode adjacent transverse magnetic mode (TM 011). When the mode frequency f is solved, the potential distribution coefficient A of each transmission line section model can be obtained i And B i
Figure BDA0003558784040000111
M as described above when the transmission line model does not take into account the rod coupler 2n The expression is simplified into：
Figure BDA0003558784040000112
When the transmission line model does not consider the rod coupler and the support rod, M is described above 2n The expression is simplified into
Figure BDA0003558784040000113
On the basis of the above theoretical calculation formula, constructing the transmission line model further requires determining the relationship between the local frequency of each acceleration unit, the equivalent inductance of the support rod, the equivalent inductance of the rod coupler, and the highest rod coupler mode (PC 01) frequency and the insertion depth of the rod coupler, which is specifically realized by the following steps:
step S11: measuring the frequency (f) of the working mode (TM 010) of a linear accelerator without a rod coupler inserted in the cavity 0 ) Taking the measured value as the local frequency (f) of all accelerating units in the transmission line model 0n )；
Step S12: according to the length L of the accelerating unit i Constructing a transmission line model for a non-strut rod and rod coupler and working mode (TM 010) frequency (f) based on the transmission line model 0 ) Local frequencies (f) of nearby sets of accelerating units 0n ) Calculating voltage distribution calculation values of a plurality of groups of accelerating units;
step S13: measuring the actual voltage distribution of each accelerating unit of the linear accelerator without inserting a rod coupler into the cavity to obtain the voltage distribution measured value of each accelerating unit, and determining the local frequency of each accelerating unit corresponding to the voltage distribution calculated value of each accelerating unit closest to the measured voltage distribution measured value of each accelerating unit as the new local frequency (f) of each accelerating unit 0n )；
Step S14: model matrix M of transmission line k Expression M at k =2n-1 2n-1 The local frequency of each acceleration unit in (1) is replaced with the new local frequency of each acceleration unit determined in step S13Frequency (f) 0n )；
Step S15: measuring the frequency of a working mode adjacent transverse magnetic mode (TM 011) of a linear accelerator cavity in a state of not inserting a rod coupler to obtain a frequency measurement value of the TM011 frequency;
step S16: in the transmission line model matrix M k Expression M at k =2n 2n In which a support rod equivalent inductance L is added s /l 0 Selecting a plurality of supporting rod equivalent inductance theoretical values according to a preset supporting rod equivalent inductance step length in a preset range above and below a supporting rod equivalent inductance theoretical value determined based on the geometric dimensions of the supporting rod and the drift tube, calculating TM011 frequency based on the supporting rod equivalent inductance theoretical values to obtain a plurality of TM011 frequency calculated values, and taking the supporting rod equivalent inductance theoretical value corresponding to the TM011 frequency calculated value closest to the TM011 frequency measured value measured in the step S15 as the supporting rod equivalent inductance of the transmission line model;
step S17: inserting each rod coupler in the cavity of the linear accelerator in a medium depth manner, measuring the mode (PC 01) frequency of the highest rod coupler of the linear accelerator and the voltage distribution of each accelerating unit, and obtaining the measured value of the mode frequency of the highest rod coupler and the voltage distribution measured value of each accelerating unit;
step S18: adding equivalent inductance of the rod coupler into the transmission line model, and converting the frequency f of each rod coupler in the transmission line model pn Setting as a measured value of the highest rod coupler mode (PC 01) frequency, selecting a plurality of rod coupler equivalent inductance theoretical values according to a predetermined rod coupler equivalent inductance step length in a predetermined range above and below a rod coupler equivalent inductance theoretical value determined based on the geometric dimensions of the rod coupler, calculating the voltage distribution of each acceleration unit based on the rod coupler equivalent inductance theoretical values to obtain a plurality of groups of voltage distribution calculated values of each acceleration unit, and taking the rod coupler equivalent inductance corresponding to the voltage distribution calculated value closest to the voltage distribution measured value of each acceleration unit measured in the step S17 as the rod coupler equivalent inductance of the transmission line model;
step S19: the method comprises the steps of inserting rod couplers with different insertion depths into a cavity of the linear accelerator, measuring a variation curve of the highest rod coupler mode (PC 01) frequency after the rod couplers are inserted into the cavity of the linear accelerator with the same insertion depth, fitting the curve, and replacing the highest rod coupler mode frequency in a transmission line model with the insertion depth of the rod couplers according to the fitted curve.
Figure 3 schematically shows the flow steps of a preferred embodiment of a field stability tuning method for an alvarez drift tube linear accelerator according to the invention.
First, in step S21: inserting the rod couplers into a cavity of the linear accelerator, setting the initial insertion depth of each rod coupler to enable the PC01 frequency measurement value in the cavity to be 2 times of the TM010 frequency measurement value and the TM011 frequency measurement value, recording the initial insertion depth of each rod coupler, and measuring the cavity tilt sensitivity to obtain the current tilt sensitivity measurement value; next, in step S22, the tilt sensitivities corresponding to all possible combinations of the insertion depths of the rod couplers selected according to the predetermined step length within the predetermined range above and below the current insertion depth of each rod coupler are calculated according to the transmission line model determined in step S1, and the insertion depth l of each rod coupler corresponding to the minimum tilt sensitivity is determined s,n (ii) a Then, in step S23, the tilt sensitivities corresponding to all possible combinations of the insertion depths of the rod couplers selected according to the predetermined step length within the predetermined range above and below the current insertion depth of each rod coupler are calculated according to the transmission line model determined in step S1, and the insertion depth l of each rod coupler corresponding to the tilt sensitivity closest to the current measurement value of the tilt sensitivity is determined e,n (ii) a Next, in step S24, the rod coupler insertion depths l corresponding to the minimum tilt sensitivities determined in step S22 are determined s,n The insertion depth l of each rod coupler corresponding to the tilt sensitivity determined in step S23 which is closest to the current measurement value of tilt sensitivity e,n Difference Δ l between n ＝l s,n -l e,n Adjusting the insertion depth of each rod coupler as an adjustment quantity, and then measuring the cavity tilt sensitivity to obtain the current measurement value of the tilt sensitivity; at this time, in step S25, the tilt sensitivity current measurement is judgedWhether the magnitude meets the requirement, if so, the adjustment of the insertion depth of each rod coupler is ended, and if not, the above-described arrangement is repeated from step S23 to step S25 based on the current insertion depth of each rod coupler (obviously, it is also conceivable to repeat from step S22).
In summary, in the tuning method for field stability of the present invention, it is first necessary to calculate the local frequency f of each acceleration unit in the transmission line model by using the measured values of the electric field and the frequency of the cavity of the acceleration cavity 0n Equivalent inductance L of the support rod s /l 0 Equivalent inductance L of rod coupler p /l 0 And then calculating the variation of the insertion depth of the rod coupler, which can enable the cavity of the accelerating cavity to be reduced from a certain inclination sensitivity state to the minimum inclination sensitivity state, by using the transmission line model, and finally realizing the tuning of the field stability through repeated iteration of the insertion depth of the rod coupler.
The field stability tuning method of the invention converts the tedious steps of repeatedly adjusting the insertion depth of the rod coupler in the prior art into the calculation problem of the transmission line model, and greatly reduces the workload, so the method steps for constructing the transmission line model are not limited to solving by a genetic algorithm or a perturbation method, and the solution of the transmission line model is not limited to the iterative calculation method disclosed in the specific implementation mode. While embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that: many changes, modifications, substitutions, variations and any combination of these embodiments may be made without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.
List of reference numerals
1. Inductance per unit length drift tube in transmission line model
2. Capacitance between unit length drift tube and cavity wall in transmission line model
3. Gap capacitance between drift tubes in transmission line model
4. Equivalent inductance of support rod in transmission line model
5. Equivalent inductance of rod coupler in transmission line model
6. Capacitance between rod coupler and drift tube in transmission line model
10. Drift tube
20. Wall of drift tube and acceleration cavity
30. Gap between drift tubes
40. Support rod
50. Rod coupler
60. A gap between the rod coupler and the drift tube.

Claims (6)

1. A field stability tuning method for an Alvarez type drift tube linear accelerator, wherein each acceleration gap of the Alvarez type drift tube linear accelerator constitutes an acceleration unit, the method comprising:
step S1: a transmission line model is constructed for the Alvarez type drift tube linear accelerator, the transmission line model enables the structures of the drift tube, the supporting rod and the rod coupler to be equivalent to impedance parameters in a transmission line equivalent circuit, and the working mode frequency (f) of a linear accelerator cavity can be obtained according to the insertion depth of each rod coupler 0 ) And an electric field distribution (V) of each accelerating element;
step S2: inserting the rod coupler into the cavity of the linear accelerator, continuously measuring the inclination sensitivity of the cavity, adjusting the insertion depth of the rod coupler according to the iterative calculation result of the constructed transmission line model from the current insertion depth of the rod coupler to the direction with the minimum inclination sensitivity until the insertion depth of each rod coupler is obtained when the inclination sensitivity meets the requirement,
it is characterized in that the preparation method is characterized in that,
the step S1 includes:
step S11: measuring the working mode frequency (f) of a linear accelerator without a rod coupler inserted into the cavity 0 ) Taking the measured values as the local frequencies (f) of all accelerating elements in the transmission line model 0n )；
Step S12: according to the length L of the accelerating unit i Constructing a non-support rod and rod couplingTransmission line model of combiner and working mode frequency (f) based on the transmission line model 0 ) Local frequencies (f) of nearby sets of accelerating units 0n ) Calculating voltage distribution calculation values of a plurality of groups of accelerating units;
step S13: measuring the actual voltage distribution of each accelerating unit of the linear accelerator without inserting a rod coupler into the cavity to obtain the voltage distribution measured value of each accelerating unit, and determining the local frequency of each accelerating unit corresponding to the voltage distribution calculated value of each accelerating unit closest to the measured voltage distribution measured value of each accelerating unit as the new local frequency (f) of each accelerating unit 0n )；
Step S14: replacing the local frequency of each acceleration unit in the transmission line model with the new local frequency (f) of each acceleration unit determined in step S13 0n )；
Step S15: measuring the frequency of the working mode adjacent transverse magnetic mode of the linear accelerator cavity in a state of not inserting the rod coupler to obtain a frequency measurement value of TM011 frequency;
step S16: adding a supporting rod equivalent inductance into the transmission line model, selecting a plurality of groups of supporting rod equivalent inductance theoretical values in a preset range above and below a supporting rod equivalent inductance theoretical value determined based on the geometric dimensions of the supporting rod and the drift tube according to a preset supporting rod equivalent inductance step length, calculating the frequency of the adjacent transverse magnetic mode of the working mode based on the groups of the supporting rod equivalent inductance theoretical values to obtain calculated values of the frequency of the adjacent transverse magnetic mode of the working mode, and taking the supporting rod equivalent inductance theoretical value corresponding to the calculated value of the frequency of the adjacent transverse magnetic mode of the working mode, which is closest to the measured value of the frequency of the adjacent transverse magnetic mode of the working mode measured in the step S15, as the supporting rod equivalent inductance of the transmission line model;
step S17: inserting each rod coupler in the cavity of the linear accelerator at medium depth, and measuring the mode frequency of the highest rod coupler of the linear accelerator and the voltage distribution of each accelerating unit to obtain the measured value of the mode frequency of the highest rod coupler and the voltage distribution measured value of each accelerating unit;
step S18: adding equivalent electricity of rod coupler into transmission line modelSensing the frequency f of each rod coupler in the transmission line model pn Setting a measured value of the mode frequency of the highest rod coupler, selecting a plurality of groups of rod coupler equivalent inductance theoretical values in a preset range above and below each rod coupler equivalent inductance theoretical value determined based on the geometric dimension of the rod coupler according to preset rod coupler equivalent inductance step lengths, calculating the voltage distribution of each accelerating unit based on the groups of rod coupler equivalent inductance theoretical values to obtain voltage distribution calculated values of the plurality of groups of accelerating units, and taking the rod coupler equivalent inductance corresponding to the voltage distribution calculated value closest to the voltage distribution measured value of each accelerating unit measured in the step S17 as the rod coupler equivalent inductance of the transmission line model;
step S19: the method comprises the steps of inserting rod couplers with different insertion depths into a cavity of a linear accelerator, measuring a change curve of the mode frequency of the highest rod coupler after the rod coupler is inserted with the same depth into the cavity of the linear accelerator along with the insertion depth of the rod coupler, fitting the curve, replacing the mode frequency of each highest rod coupler in a transmission line model with the insertion depth of the rod coupler according to the fitted curve,
the step S2 includes:
step S21: inserting the rod couplers into a cavity of the linear accelerator, recording the initial insertion depth of each rod coupler, and measuring the inclination sensitivity of the cavity to obtain the current measurement value of the inclination sensitivity;
step S22: calculating tilt sensitivities corresponding to all possible combinations of the insertion depths of the rod couplers selected according to a preset step length in a preset range above and below the current insertion depth of each rod coupler according to the transmission line model constructed in the step S1, and determining the insertion depth l of each rod coupler corresponding to the minimum tilt sensitivity s,n ；
Step S23: calculating tilt sensitivities corresponding to all possible combinations of the insertion depths of the rod couplers selected according to the preset step length in the preset range above and below the current insertion depth of each rod coupler according to the transmission line model determined in the step S1, and determining the insertion depth l of each rod coupler corresponding to the tilt sensitivity closest to the current measurement value of the tilt sensitivities e,n ；
Step S24: the insertion depth l of each rod coupler corresponding to the minimum tilt sensitivity determined in step S22 s,n The insertion depth l of each rod coupler corresponding to the tilt sensitivity determined in step S23 that is closest to the current measurement value of tilt sensitivity e,n Difference Δ l between n Adjusting the insertion depth of each rod coupler as an adjustment quantity, and then measuring the cavity tilt sensitivity to obtain the current measurement value of the tilt sensitivity;
step S25: and judging whether the current measurement value of the inclination sensitivity meets the requirement, if so, finishing the adjustment of the insertion depth of each rod coupler, and if not, repeating the steps from the step S22 or S23 to the step S25 based on the current insertion depth of each rod coupler.
2. The field stability tuning method of claim 1, wherein in step S13, a voltage distribution calculation value of each acceleration cell closest to the measured voltage distribution measurement value of each acceleration cell is determined based on a genetic algorithm or an intrinsic perturbation method from among the voltage distribution calculation values of the sets of each acceleration cell calculated in step S12.
3. The field stability tuning method of claim 1, wherein in step S21, all rod couplers are inserted equally deep at the same initial insertion depth.
4. The method of claim 3, wherein in step S21, the initial insertion depth is set such that the highest rod coupler mode frequency measurement in the cavity is 2 times the difference between the operating mode frequency measurement and the operating mode adjacent transverse magnetic mode frequency measurement.
5. The field stability tuning method of claim 3, wherein in step S22, only tilt sensitivities corresponding to combinations of non-calculated insertion depths of all possible combinations of insertion depths of rod couplers selected by a predetermined step size within a predetermined range above and below the current insertion depth of each rod coupler are calculated and compared with the current minimum tilt sensitivity to determine a new minimum tilt sensitivity.
6. The field stability tuning method of claim 1, wherein in step S25, the tilt sensitivity current measurement value is required to be less than or equal to the tilt sensitivity target value, or the tilt sensitivity current measurement value has been reduced by less than a predetermined reduction amount relative to the tilt sensitivity current measurement value prior to performing the adjustment of step S24.
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US5578909A (en) * 1994-07-15 1996-11-26 The Regents Of The Univ. Of California Coupled-cavity drift-tube linac
ITMI20022608A1 (en) * 2002-12-09 2004-06-10 Fond Di Adroterapia Oncologic A Tera LINAC WITH DRAWING TUBES FOR THE ACCELERATION OF A BAND OF IONS.
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