CN115175433A - Solenoid beam cluster confinement model and charged particle beam cluster current compression method - Google Patents
Solenoid beam cluster confinement model and charged particle beam cluster current compression method Download PDFInfo
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- CN115175433A CN115175433A CN202210705259.0A CN202210705259A CN115175433A CN 115175433 A CN115175433 A CN 115175433A CN 202210705259 A CN202210705259 A CN 202210705259A CN 115175433 A CN115175433 A CN 115175433A
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Abstract
The application provides a solenoid beam group confinement model and a charged particle beam group current compression method, and relates to the technical field of accelerator charged particle beam current compression, wherein the model comprises the following steps: a main solenoid assembly for forming a uniform magnetic field inside the solenoid; the introducing component is used for sequentially introducing the charged particle beam clusters into the uniform magnetic field so that the charged particle beam clusters move spirally; the confinement region component is similar to a magnetic mirror structure in function, and restrains charged particles which are sequentially incident in a reciprocating spiral motion in a confinement region until the flow uniformity and flow strength in the confinement region reach preset values; and the leading-out assembly is used for leading out the charged particle beam with average current intensity reaching a preset value from the confinement model. The invention multiplies the beam cluster number and the average current in the confinement model by making the charged particle beam cluster reciprocate in the confinement region, and solves the problems that the charged particle beam current compression device has large volume and high cost, and the average current of the compressed beam can only reach mA magnitude.
Description
Technical Field
The application relates to the technical field of accelerator charged particle beam current compression, in particular to a solenoid beam cluster confinement model and a charged particle beam cluster current compression method.
Background
Charged particle beams generated by the accelerator have the characteristics of strong controllability and stability, and are widely applied in the fields of medical treatment, industry and scientific research. However, the development of the leading edge science at present generates the demand for high-energy charged particle beam with higher current intensity (kA), which is beneficial to the fact that the Z pinch in nuclear fusion research can utilize high-energy electron beams with the magnitude of average current-kA to bombard a fusion target to ignite, but if photocathode electrons with the magnitude of kA average current are directly accelerated to 10MeV in a traditional mode, a klystron or a magnetron which needs the average power of tens of megawatts is used for supplying energy to an accelerating tube, only pulse power of tens of megawatts can be supplied according to the development level of the current klystron, and for the ignition of the Z pinch, ten thousand klystrons are required to work simultaneously to possibly meet the power demand, and the cost cannot be imagined. In addition, the beam interval of the charged particles is also limited by the charged particle emission source, and it is difficult to directly generate a charged particle beam having a repetition frequency of 10 GHz.
Therefore, the charged particle beam with low repetition frequency and low average current intensity is accelerated to the specified energy by utilizing the accelerating structure, and then the electron beam interval is compressed, so that the purpose can be achieved with acceptable cost. The CTF3 device of the CLIC is a typical electron beam group average current compression device, a preamble structure firstly accelerates 3 GHz-repetition-frequency electron beams to 350MeV, then the beam groups are sequentially injected into a combination ring, the compressed electron beam group interval is compressed to 33ps from 333ps, the repetition frequency reaches 30GHz, the power of the electron beams reaches ten times of that before compression, and then the electron beams are led out to a tail field acceleration structure to accelerate colliding particles. In addition to this way of increasing the repetition frequency of electron bunches, the storage ring is also a common mean current compression device for charged particles, and is different in that the electron bunches injected successively converge into the same bunch, rather than being spaced and reduced, until the bucket phase space is filled, and after the expected mean current is reached, the charged particles can be led out to the subsequent structure.
However, in the charged particle beam compression method of the related art, both the CTF3 and the storage ring have the limitations of large volume and high cost, and the maximum achievable average current intensity is limited by the parameters of the ring, and the average current of the electron beam group in the storage ring can only reach the mA magnitude and far cannot meet the application requirements of Z pinch and the like.
Disclosure of Invention
The application provides a solenoid beam bunch confinement model and a charged particle beam bunch current compression method, which aim to solve the problems that in the related art, the charged particle beam compression is realized by using a CTF3 and a storage ring, the size is large, the cost is high, the average current of an electron beam bunch in the storage ring can only reach the mA magnitude, and the requirements of applications such as Z pinch cannot be met.
A first aspect of the present application proposes a solenoid beam confinement model, comprising: a main solenoid assembly for forming a uniform magnetic field inside the solenoid; the introducing component is used for sequentially introducing a plurality of charged particle beam clusters into the uniform magnetic field so as to enable the charged particle beam clusters to make spiral motion; the confinement region component is used for enabling the charged particle beam clusters which are sequentially incident to perform reciprocating spiral motion between the reflecting magnet pairs until the flow average intensity of the charged particle beam reaches a preset value; and the leading-out assembly is used for leading out the charged particle beam with the average current intensity reaching a preset value from the confinement model.
Further, the main solenoid assembly comprises a ferromagnetic material shielding shell, an aluminum barrel, a ferromagnetic material support column and a main coil, wherein the ferromagnetic material support column is used for fixing a plurality of magnet elements inside the main solenoid and forms a magnetic circuit together with the ferromagnetic material shielding shell.
Further, the introduction assembly includes:
an introduction aperture for introducing the plurality of charged particle clusters;
and introducing a magnet for causing the introduced charged particle beam cluster to move spirally with a solenoid axis as a central axis.
Further, the confinement region assembly comprises:
the induction side reflecting magnet is used for switching off current when the charged particle beam group passes through the induction side reflecting magnet, and switching on current after the charged particle beam group passes through the induction side reflecting magnet to ensure that incident electrons can enter a confinement region and provide deflection force for the beam group in confinement so as to ensure that the charged particle beam group introduced in sequence reciprocates spirally in the confinement region;
the focusing magnet is used for providing a gradient field and improving the stability of the reciprocating spiral motion of the charged beam group;
the leading-out side reflecting magnet is used for providing a reverse deflection force for the beam group in confinement so as to ensure that the beam group can perform reciprocating spiral motion between the leading-in side reflecting magnetic strip and the leading-out side reflecting magnet; and when the flow average current intensity of the charged particle beams in the confinement interval reaches a preset value, cutting off the current, so that the charged particle beams spirally move to the leading-out assembly.
Further, the extraction assembly comprises: the leading-out hole and the leading-out magnet are used for leading out the charged particle beam with average flow strength reaching a preset value.
A second aspect of the present application proposes a method of current compression of a charged particle beam of an accelerator applied to the solenoid beam confinement model of the first aspect, the method comprising:
forming a uniform magnetic field inside the solenoid;
sequentially introducing a plurality of charged particle beam clusters into the uniform magnetic field so that the charged particle beam clusters move spirally;
enabling the charged particle beam clusters which are sequentially incident to perform reciprocating spiral motion between the reflecting magnet pairs until the leveling average intensity of the charged particle beams in the confinement interval reaches a preset value;
and leading out the charged particle beam with average current intensity reaching a preset value from the confinement model.
Further, the reciprocating spiral motion of the charged particle beam cluster between the pair of reflecting magnets until the average current intensity of the charged particle beam cluster reaches a preset value includes:
after the charged particle beam group enters the confinement region, the charged particle beam group is incident at an axial incident velocity v z0 Spirally moving to the leading-out side reflecting magnet;
the charged particle beam group is led out of the side reflection magnetActs in reverse at an axial velocity-v z0 Spirally moving to the introduction-side reflection magnet;
and the flow average intensity of the charged particle beam group in the confinement region from reciprocating spiral motion to the confinement region reaches a preset value.
Further, if the time interval before the introduction of the adjacent cluster is T b Before reaching the leading-out assembly, the difference of the reciprocating cycle numbers in the confinement region assembly is n, and when reaching the leading-out assembly, the adjacent beam group interval is as follows:
T′ b ＝T b -nNT c
wherein N is the number of turns of the back and forth spiral motion of the charged particle beam group in the confinement region, and T is the number of turns of the back and forth spiral motion of the charged particle beam group in the confinement region c The charged particle beam group is in a convolution period of spiral motion in the uniform magnetic field.
Optionally, when the charged particle beam bunch is led out, the compression times of the repetition frequency and the average current of the charged particle beam bunch compared to the led-in time are as follows:
wherein, T b The beam group interval when the charged particle beam groups enter the leading-in assembly, N is the number of turns of the charged particle beam group reciprocating a back-and-forth spiral motion in the confinement region, and T c The period of the charged particle beam group doing spiral motion in the uniform magnetic field is the convolution period, and n is the difference of the period of the adjacent beam group reciprocating motion in the confinement region assembly before reaching the leading-out assembly.
The technical scheme provided by the embodiment of the disclosure at least brings the following beneficial effects:
the charged particle beam group can stably and spirally move after being introduced into a uniform field in the solenoid, the beam group can be confined in the structure by controlling the deflection magnet which controls the electron beam group to be reflected back and forth in the confinement region, meanwhile, the beam group is sequentially injected into the structure, the power supply of the deflection magnet coil is controlled to be instantly turned off during the beam group injection, the deflection magnet coil is rapidly turned on after the injection is finished, and the beam group in the structure is continuously reflected, so that the number and the current of the beam group in the confinement structure are multiplied, when the beam intensity in the structure reaches a set value, the current of the magnet at the leading-out side is turned off, the compressed beam current can be sequentially led out, the compression of the charged particle beam is realized, the current compression of the charged accelerator particle beam with the kA-level average current is realized, the structure is compact, and the requirements of applications such as Z pinch are met.
Additional aspects and advantages of the present application will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the present application.
Drawings
The foregoing and/or additional aspects and advantages of the present application will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a schematic diagram of a solenoid beam confinement model according to an embodiment of the present disclosure;
FIG. 2 is a flow chart of a method for compressing a current of a charged particle beam of an accelerator according to an embodiment of the present application;
FIG. 3 is a flow chart of a method for compressing a current of a charged particle beam of an accelerator according to an embodiment of the present application;
FIG. 4 is a schematic diagram illustrating a charged particle beam confinement principle according to an embodiment of the present disclosure;
FIG. 5 is a schematic diagram of a charged particle beam bunch time structure before and after compression according to an embodiment of the present disclosure;
fig. 6 is a schematic diagram of field strength changes when the leading-in side reflected magnet and the leading-out side reflected magnet are electrified with time-varying current according to the embodiment of the application.
Detailed Description
Reference will now be made in detail to embodiments of the present application, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are exemplary and intended to be used for explaining the present application and should not be construed as limiting the present application.
Fig. 1 is a schematic structural diagram of a solenoid beam confinement model according to an embodiment of the present disclosure.
In this embodiment, as shown in fig. 1, a main solenoid assembly is used to create a uniform magnetic field inside a solenoid, wherein the main solenoid assembly comprises: the electromagnetic solenoid comprises a ferromagnetic material shielding shell 1, an aluminum barrel 2, a ferromagnetic material support 3 and a main coil 4, wherein the ferromagnetic material support 3 is used for fixing a plurality of magnet elements inside the main solenoid and forms a magnetic circuit together with the ferromagnetic material shielding shell 1.
The introducing assembly 5 is used for sequentially introducing a plurality of charged particle beam clusters into the uniform magnetic field, so that the charged particle beam clusters make spiral motion, wherein the introducing assembly comprises: an introducing hole 10 and an introducing magnet 11, wherein the introducing hole 11 is used for introducing a plurality of charged particle beam groups, and the introducing magnet 12 is used for enabling the introduced charged particle beam groups to make spiral motion by taking a solenoid shaft as a central shaft.
The confinement region component is used for enabling the charged particle beam group to perform reciprocating spiral motion between the pair of reflecting magnets until the flow intensity of the charged particle beam reaches a preset value, wherein the confinement region component comprises: a leading-side reflection magnet 7, a leading-side reflection magnet 8, and a focusing magnet 9.
The leading-in side reflecting magnet 7 turns off the current when the charged particle clusters pass through the leading-in side reflecting magnet, and turns on the current after the charged particle clusters pass through the leading-in side reflecting magnet, thereby ensuring that the sequentially incident beam clusters can be led into the confinement region.
After entering the confinement interval, the bunch continues to move spirally to the leading-out side reflection magnet 8, and then moves spirally toward the leading-in side reflection magnet in the reverse direction after receiving the deflection force, and when the bunch in the confinement interval passes through the leading-in side reflection magnet, the current is in the on state, so that the bunch is deflected and then moves spirally toward the leading-out side reflection magnet. This is repeated. The beam groups are sequentially introduced into the space between the pair of reflecting magnets and are confined in the space by the pair of reflecting magnets, so that the number of the beam groups subjected to confinement action and reciprocating motion in the space is gradually increased.
The leading-out side reflecting magnet 8 provides a reverse deflection force for the bunches in the forbidden region, and ensures that the bunches can do reciprocating spiral motion between the leading-in side reflecting magnetic strip and the leading-out side reflecting magnet; and when the flow average current intensity of the charged particle beams in the confinement interval reaches a preset value, cutting off the current to enable the charged particle beams to spirally move to the leading-out assembly. And then the uniform motion is carried out to a subsequent device by the leading-out component.
And the focusing magnet 9 is used for providing a gradient field and improving the stability of the spiral reciprocating motion of the charged beam group in the confinement region.
The leading-in magnet 7, the leading-out magnet 8, and the focusing magnet 9 are all coil magnets, and the inside of the solenoid is vacuum.
The leading-out component 6 is of an electronic leading-out structure and comprises a leading-out hole and a leading-out magnet and is used for leading out charged particle clusters with average flow strength reaching a preset value, and the leading-out component 6 and the leading-in component 5 are symmetrically arranged.
According to the solenoid beam cluster confinement model provided by the application, the charged particle beam cluster can stably perform spiral motion after being introduced into a uniform field in the solenoid, and the introduced beam cluster can be confined in the structure by controlling the current of the deflection magnets on two sides of the confinement region. When beam groups are injected into the structure in sequence, the power supply of the deflection magnet coil is controlled to be turned off instantly when the beam groups are injected, the deflection magnet coil is turned on quickly after the injection is finished, and the beam groups in the confinement structure are continuously reflected, so that the number of the beam groups and the average current in the confinement structure are multiplied, when the beam intensity in the structure reaches a set value, the current of the magnet at the extraction side is turned off, the compressed beam can be extracted in sequence, the compression of the charged particle beam is realized, and the current compression of the accelerator charged particle beam with the kA-level average current is realized. The device has compact structure, and can compress relativistic charged particle beams to extremely high current intensity.
Fig. 2 is a flowchart of a method for compressing a current of a charged particle beam of an accelerator according to an embodiment of the present application. As shown in fig. 2, the method comprises the steps of:
103, enabling the charged particle beam clusters which are sequentially injected to perform reciprocating spiral motion between the reflecting magnet pairs until the leveling strength of the charged particle beams in the confinement interval reaches a preset value;
and 104, leading out the charged particle beam group with the average flow strength reaching a preset value from the confinement model.
With regard to the methods in the above-described embodiments, the specific manner in which each method performs an operation has been described in detail in the embodiments related to the model, and will not be explained in detail here.
Fig. 3 is a flowchart of a method for compressing a current of a charged particle beam of an accelerator according to an embodiment of the present application, where as shown in fig. 3, step 103 further includes:
As shown in fig. 4, wherein the charged particle beam mass continues to have an axial velocity v after entering the confinement region z The spiral movement is performed for N/2 periods to the leading-out side reflecting magnet 8, and after the deflecting force is applied, the direction is reversed again to form an axial speed-v z Spiral N/2 cycles to the leading-in side reflection magnet 7, and repeating the above steps, wherein the duration of each confinement period is NT C Wherein v is z The vector velocity of the charged particle beam group is the incident vector velocity, N is the number of turns of the electron to and fro one round trip in the confinement region, and can be any positive or even number according to the design.
Further, if the time interval before the introduction of the adjacent cluster is T b Before reaching the leading-out assembly, the difference of the reciprocating cycle number in the confinement region assembly is n, and when reaching the leading-out assembly, the interval between adjacent bunches is as follows:
T′ b ＝T b -nNT c
wherein N isThe charged particle beam group makes a reciprocating spiral motion in the confinement region for a number of turns, T c Is the convolution period of the helical motion of the charged particle beam cluster in the homogeneous magnetic field.
Further, the compression factor of the repetition frequency and the average current of the charged particle beam mass at the time of extraction compared to the time of introduction is:
wherein, T b The interval of a plurality of charged particle beam groups when entering the leading-in assembly, N is the number of turns of the charged particle beam group reciprocating a back-and-forth spiral motion in the confinement region, T c The period of the charged particle beam group in the uniform magnetic field is the convolution period of the spiral motion, and n is the number of circles of the difference of the reciprocating motion periods of the adjacent beam groups before reaching the leading-out assembly and in the confined area assembly.
The accelerator charged particle beam current compression method will be explained with reference to a specific example, which achieves 10 times current compression of a 10-charge 1nC, 6.511MeV electron beam.
(1) 10 electron bunches spaced 48ns apart, of charge 1nC, with energy 6.511MeV were introduced into the solenoid structure (as shown in fig. 1). According to the design, the shimming field intensity of the solenoid is about 0.1T, the radius of the spiral motion track of the electron beam group is 25cm, and the motion period is 5.4ns. Other relevant parameters: the inner diameter of the solenoid is 40cm, and the distance between the leading-in side reflecting magnets and the leading-out side reflecting magnets is 150cm.
(2) The lead-in and lead-out side reflection magnets are energized with a time-varying current, the field intensity of which changes as shown in fig. 6, and the magnetic field of the lead-in side reflection magnet 7 is incident at an electron incidence interval T b And =48ns is a period for instantaneous turn-off, the turn-off time at each time is Δ t =0.2ns, the leading-out side reflecting magnet 8 is normally open at the earlier stage, and 10 bunches are preset to be turned off after all the bunches enter a confinement interval.
(3) The periods of adjacent beam groups moving between the reflecting magnet pairs are sequentially different by 1, and when the adjacent beam groups reach the extraction structure, the charged particle beam group interval T' b ＝T b -nNT c =4.8ns, repetition frequency and average powerThe current is up to 10 times the incident time, achieving 10 times the average current compression.
It should be noted that the foregoing explanation of the embodiment of the solenoid beam confinement model is also applicable to the current compression method of the accelerator charged particle beam of this embodiment, and will not be described herein again.
According to the accelerator charged particle beam current compression method provided by the application, a charged particle beam group can stably perform spiral motion after being introduced into a uniform field in a solenoid, the beam group can be confined in a structure by controlling a deflection magnet which reflects the electron beam group in a reciprocating manner in a confinement region, the beam group is injected into the structure in sequence, a deflection magnet coil power supply is controlled to be turned off instantly after the beam group is injected, the deflection magnet is turned on rapidly after the injection is completed, and the beam group in the structure is reflected continuously, so that the number of the beam groups and the current in the confinement structure are multiplied, when the beam intensity in the structure reaches a set value, the magnet current at the extraction side is turned off, the compressed beam can be extracted in sequence, the compression of the charged particle beam is realized, the accelerator charged particle beam current compression of the kA-level average current is realized, the structure is compact, and the requirements of applications such as Z pinch are met.
In the description herein, reference to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the application. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or N embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present application, "N" means at least two, e.g., two, three, etc., unless explicitly defined otherwise.
Although embodiments of the present application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present application, and that variations, modifications, substitutions and alterations may be made to the above embodiments by those of ordinary skill in the art within the scope of the present application.
Claims (9)
1. A solenoid beam confinement model, comprising:
a main solenoid assembly for forming a uniform magnetic field inside the solenoid;
an introducing component, which is used for sequentially introducing a plurality of charged particle beam clusters into the uniform magnetic field so that the charged particle beam clusters move spirally;
the confinement region component is used for enabling the charged particle beam clusters which are sequentially incident to perform reciprocating spiral motion between the reflecting magnet pairs until the leveling flow strength of the charged particle beam clusters reaches a preset value;
and the leading-out assembly is used for leading out the charged particle beam with average current intensity reaching a preset value from the confinement model.
2. The apparatus of claim 1, wherein the main solenoid assembly comprises a shield case of ferromagnetic material, an aluminum cylinder, a pillar of ferromagnetic material, and a main coil, wherein the pillar of ferromagnetic material is used for fixing a plurality of magnet elements inside the main solenoid and constitutes a magnetic circuit together with the shield case of ferromagnetic material.
3. The apparatus of claim 1, wherein the introduction assembly comprises:
an introduction aperture for introducing the plurality of charged particle clusters;
and introducing a magnet for spirally moving the introduced charged particle beam cluster with the solenoid axis as a central axis.
4. The apparatus of claim 1, wherein the confinement region assembly comprises:
the induction side reflecting magnet is used for switching off current when the charged particle beam group passes through the induction side reflecting magnet, and switching on current after the charged particle beam group passes through the induction side reflecting magnet to ensure that incident electrons can enter a confinement region and provide deflection force for the beam group in confinement so as to ensure that the charged particle beam group introduced in sequence reciprocates spirally in the confinement region;
the focusing magnet is used for providing a gradient field and improving the stability of the reciprocating spiral motion of the charged particle beam group;
the extraction side reflecting magnet is used for providing a reverse deflection force for the beam group in the forbidden region and ensuring that the beam group can perform reciprocating spiral motion between the extraction side reflecting magnet and the extraction side reflecting magnet; and when the flow average current intensity of the charged particle beams in the confinement interval reaches a preset value, cutting off the current, so that the charged particle beams spirally move to the leading-out assembly.
5. The apparatus of claim 1, wherein the extraction assembly comprises: the leading-out hole and the leading-out magnet are used for leading out the charged particle beam with average flow strength reaching a preset value.
6. A method of current constriction of a charged particle beam of an accelerator applied to a solenoidal confinement model according to any of claims 1 to 5, comprising:
forming a uniform magnetic field inside the solenoid;
sequentially introducing a plurality of charged particle beam clusters into the uniform magnetic field so that the charged particle beam clusters move spirally;
enabling the charged particle beam clusters which are sequentially incident to perform reciprocating spiral motion between the reflecting magnet pairs until the leveling average intensity of the charged particle beams in the confinement interval reaches a preset value;
and leading out the charged particle beam with average current intensity reaching a preset value from the confinement model.
7. The method of claim 6, wherein said back and forth spiraling of said charged particle beam mass between said pair of repellers until said charged particle beam mass mean current strength reaches a predetermined value comprises:
after the charged particle beam group enters the confinement region, the charged particle beam group is incident at an axial incident velocity v z0 Spirally moving to the leading-out side reflecting magnet;
the charged particle beam is acted by the deflection force of the reflection magnet at the extraction side and reversely rotates at an axial speed-v z0 Spirally moving to the introduction-side reflection magnet;
and the flow average intensity of the charged particle beam group in the confinement region from reciprocating spiral motion to the confinement region reaches a preset value.
8. The method of claim 6, wherein the time interval before introduction of adjacent clusters is T b Before reaching the leading-out assembly, the difference of the reciprocating cycle number in the confinement region assembly is n, and when reaching the leading-out assembly, the interval between the adjacent bunches is as follows:
T′ b ＝T b -nNT c
wherein N is the number of turns of the back-and-forth spiral motion of the charged particle beam group in the confinement region, and T is c A convolution period during which said charged particle beam cluster makes a helical motion in said homogeneous magnetic field.
9. The method of claim 6, wherein the compression factor of the charged particle beam mass repetition frequency and average current at extraction compared to that at introduction is:
wherein, T b Bunching the plurality of charged particlesThe interval of the charged particle beam group when the charged particle beam group enters the leading-in assembly, N is the number of turns of the charged particle beam group which makes a back-and-forth spiral motion in the confinement region, and T is the number of turns of the charged particle beam group which makes a back-and-forth spiral motion c The period of the charged particle beam group doing spiral motion in the uniform magnetic field is the convolution period, and n is the difference of the period of the adjacent beam group reciprocating motion in the confinement region assembly before reaching the leading-out assembly.
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