CN1507310A - Anti-Liouville's theorem strong-damping charged particle storing ring in non-Hamiltonian mechanical system - Google Patents

Abstract

In the anti-Liouville's theorem strong-damping charged particle storing ring in non-Hamiltonian mechanical system, the charged particle moving between two polar irons has horizontal free vibration, which does not comply with Liouville's theorem of conservative phase space phase volume while comply with anti-Liouville's theorem of constantly reduced phase space phase volume. This kind of guide magnetic iron has the functions of both strong damping and fast cooling, and may be arranged into storing ring in certain period alone or via combination with four polar irons or other focusing element. The beam flow emittance may be contracted fast to raise brightness, to realize the continuous implantation of beam flow, and to realize the nuclear reaction of various charged particles and thermonuclear fusion.

Description

The anti-Liouville's theorem heavy damping of non-Hamilton's mechanical system charged particle storage rings

The invention belongs to the charged particle accelerator field, be specifically related to a kind of charged particle line storage rings.

Storage rings are to utilize electromagnetic field that charged particle is constrained in several centimetres of bores or the bigger ring vaccum pipeline, make it constantly do shuttling movement, thereby can keep several hrs even longer time.In ring vaccum pipeline outside, periodic arrangement has four utmost points and dipolar magnet, and each periodic unit is called Lattice[1].The former produces the focusing force of vertical direction or horizontal direction, to overcome the Coulomb repulsion between the charged particle, makes it unlikelyly strike on the vacuum pipe wall and lose.The main effect of two utmost point iron is to make beam bending, therefore is also referred to as guidance magnets, and the particle beams is constantly rotated along circular orbit.

The operation principle of storage rings is [2] that are based upon on the alternating gradient alternating-gradient theory basis of Courant and Snyder.The product of maximum subtended angle of the particle beams and beam diameter half width is called beam emittance.According to above-mentioned theory, beam emittance remains a constant in motion process, promptly claims the emittance conservation.The two dimension emittance can be expressed as an ellipse, and along on the storage rings diverse location in one week, major and minor axis that this is oval and inclination angle are constantly changing; But it is constant that oval area remains, and is the image statement of this conservation theorem.Particularly in permanent electromagnetostatic field, under the condition that particle energy remains unchanged, resemble the various periodic units described in the literary composition [1], beam emittance is dwindled.That is to say that it does not have any damping or cooling effect to existing storage rings itself.

The emittance conservation is the serious hindrance that can not cross over realizing that line injects continuously.To the particle beams of injector generation be injected in the vacuum pipe of storage rings, must push line to pipe interior [1] through a device that generates an electromagnetic field.This device generally is made up of deflector and cutter two parts.Be in the cutter that is called between injected beam and the trunk line circulation line, mainly work to separate both.In motion process, when emittance can not get shrinking, line will inevitably strike once more on the cutter and lose.Usually can only realize that single injects, seriously hinder the strong raising of the total stream of storage rings.

The emittance conservation is the serious restriction that beam luminosity is improved.Beam intensity in the unit solid angle is called brightness.It is directly proportional by force with total stream, is inversely proportional to emittance.Because injecting, single limited the strong further raising of total stream.Under the condition of emittance conservation, brightness also can't improve so.High brightness is to build the leading indicator [1] that storage rings are pursued.

In order to improve the strong and brightness of stream, need repeatedly injection to make line obtain accumulation at storage rings.As process of describing in the literary composition [1], the line that must make new injection is through repeatedly damping, makes after its storage bundle in trunk line is fused to fully, could begin the new injection of another time and circulate.Because storage rings itself do not have any damping or cooling effect, must just can make the line of new injection obtain effective damping by means of additional in addition cooling effect.The speed of existing various cooling meanss is compared with the swing circle of particle, and is much lower, generally needs through after the circles up to ten thousand, could begin the new injection circulation of another time.This just makes the accumulation efficient of line in storage rings greatly reduce.How to improve cooldown rate, realize the continuous injection of line, even be the unsolved so far great difficult problems of the mankind.

Beam emittance is dwindled be called damping or line cooling.Line cooling means commonly used at present has following several;

One, adiabatic cooling also claims adiabatic damping [3].When particle was subjected to high-frequency electric field and quickens synchronously, particle energy constantly increased thereupon, and according to the theory of relativity theory, mass particle increases thereupon, and beam emittance also shrinks thereupon.

Two, synchrotron radiation cooling.Mainly occur in the positron-electron storage rings.Because positron-electron when the place of experience two utmost point iron, is subjected to the Luo Lun magneticaction and track is bent, and produces bremstrahlen simultaneously, makes emittance shrink [3].

Three, electron beam cooling.In positive antiproton and heavy ion storage rings, add an electron beam.When electronics was identical with ion average speed, when observing in the inertia coordinate system that advances with this speed, electronics and ion were equivalent to two kinds of gases that temperature is inequality.When the energy spread of electron beam and emittance during less than the ion beam respective amount, heat exchange takes place and trends towards balance in both, and ion beam obtains cooling [3].

Four, cooling at random.Its basic principle is similar to automatic control.Promptly on a certain azimuth of storage rings, settle a detector, detect signal control at a distance of the electromagnetic field generator that place, certain azimuth settles, constantly particle is corrected on the equilibrium orbit, statistics shows for a long time, the particle emission degree can shrink, and energy spread also can reduce [3].

Five, the nonlinear dampling of edge focusing.State Intellectual Property Office of the People's Republic of China discloses our last invention, the patent No. is [00107730.9] " edge-focusing non-linear damp storage ring ", be to utilize the edge focusing angle of two utmost point guidance magnets greater than zero, perhaps satisfy and hang most under the condition of damping, make two utmost point guidance magnets have both the effect of cooler at it.Simultaneously, in constant electromagnetic field, make the work of storage rings be not only stable with other concentrating element reasonable combination such as four utmost point iron; And beam emittance can be shunk rapidly, improves brightness.

Except the bright edge-focusing non-linear damp storage ring of Wo Hair, all said method cooling effectivenesss are not high, can't realize the continuous injection [3] of line so far.Up to the present, the mankind have built many storage rings, and a fundamental drawback is exactly that emittance can not be shunk.Particularly in permanent electromagnetostatic field, under the condition that particle energy remains unchanged,,, people how emittance to be shunk with two utmost point iron even not understanding although four utmost point iron and two utmost point iron have various various combination designs [1].When magnetic field is subjected to along with particle that high-frequency electric field quickens synchronously and when rising, above-mentioned adiabatic cooling can occurs; But the structure-irrelevant of it and two utmost point iron is that particle energy increases and the adjection that occurs.In the patent No. is in " edge-focusing non-linear damp storage ring " of [00107730.9], and we find that first two utmost point iron edge focusings have a kind of damping action under nonlinear condition, or claims that line cools off automatically.But, the Liouville's theorem of Hamilton's mechanical system canonical phase space phase volume conservation is still observed in its horizontal free oscillation, limited the effect of edge focusing nonlinear dampling, therefore it can not independently use, must with other concentrating element reasonable combination such as four utmost point iron, could be in constant electromagnetic field, the work that makes storage rings is stable.Owing to other concentrating elements such as being subjected to four utmost point iron causes the interference that emittance is expanded, give and realize that the continuous injection of line brings technical numerous difficulties.

The objective of the invention is to, the anti-Liouville's theorem heavy damping of a kind of non-Hamilton's mechanical system storage rings are provided.

Theoretical foundation of the present invention is: the anti-Liouville's theorem of non-Hamilton's mechanical system.

When introducing the line cooling, A.N.Skrinsky says: " utilization does not rely on any external electromagnetic field of intrafascicular specified particle motion, can not make the line phase density obtain increasing.In this case, the line phase density of Tong Chang Suo Said is constant and determines that by initial condition (Liouville's theorem) set up." [3] this that is to say the phase part of the line that in constant electromagnetic field, moves long-pending be can not be shrinkable.This is confirmed by a large amount of scientific practice of Er ten Ji From accelerator, does not find exception in the accelerator experiment so far as yet.But, must be pointed out that it is with good conditionsi that Liouville's theorem is set up, in Hamilton's mechanical system, set up, people did not do research to non-Hamilton's mechanical system so far as yet, failed to investigate anti-Liouville's theorem yet.

D.T.Greenwood is at explanation Said during Liouville's theorem:the necessary condition that Liouville's theorem is set up is " the Jacobian determinant of putting corresponding conversion mutually do not have zero point; And the conversion of hiding mutually of also just anticipating is one to one, and is implying equation of motion uniqueness of solution. " [4]. The above-mentioned argumentation of Greenwood illustrates the necessary condition that the bright Liouville's theorem of people Zao Yi is set up just; Distinguishes the criterion of Hamilton's mechanical system and non-Hamilton's mechanical system just.The necessary condition that the anti-Liouville's theorem that non-Hamilton's mechanical system phase space phase volume is dwindled is set up:the one; Equation of motion group particular solution has a Jian Jin Line, that is to say that the uniqueness theorem of solving the equation is false; The 2nd, must organize the equilibrium orbit that a certain Tiao Qu Line in the particular solution is elected to be reference orbit or usual Suo Said to this; In this case, because Jian Jin Line has the characteristic of secondary contact at least on one point, the corresponding Jacobian determinant that can prove the phase point transformation has a zero point, just meaning also that mutually conversion concerns one to one is false, and that is to say that three main points of the above statement of D.T.Greenwood can obtain strict proof.The result shows that corresponding Hamilton's equation is interdependent, and the phase volume in a certain zone of phase space of transverse movement is shunk, and is called the anti-Liouville's theorem of non-Hamilton's mechanical system that the phase space phase volume is dwindled.This shows that the necessary condition that Hamilton's mechanical system Liouville's theorem is set up is just in time opposite with the necessary condition that the anti-Liouville's theorem of non-Hamilton's mechanical system is set up, and says that as D.T.Greenwood under the condition that Liouville's theorem is set up, anti-Liouville's theorem is false; Vice versa, and under the condition that anti-Liouville's theorem is set up, Liouville's theorem is false.Liu Wei only finishes half of whole work, another prior half, be that we finish, this is necessary complement and development to the Liouville's theorem of setting up in 1838.

In order to check the correctness and the generality of the anti-Liouville's theorem of non-Hamilton's mechanical system, we have discussed Distribution of Magnetic Field on the magnetic blow out centre plane is particle movement under the unidirectional uniform situation.In cartesian coordinate system, Distribution of Magnetic Field vertically is uniform on the central plane, along continuous straight runs and cycle change, for simple Qi Inter, suppose that cycle variation And requires have a Jian Jin Line And that the Tiao Qu Line this group particular solution is elected to be reference orbit or usual said equilibrium orbit from the horizontal direction parallel incident beam according to SIN function in an along continuous straight runs distribution, for convenience therebetween, being elected to be equilibrium orbit from initial point and the particle Rail Trace that is parallel to horizontal axis incident, the lateral coordinates of corresponding natural system of coordinates and corresponding canonical momentum are formed a canonical phase plane.Equal one from the corresponding Jacobian determinant of the initial infinitesimal transformation of the parallel beam of horizontal direction incident; And it is a zero point to the corresponding Jacobian determinant of the corresponding phase point transformation of Jian Jin Line, so, less than one, illustrate that the anti-Liouville's theorem of non-Hamilton's mechanical system that phase volume is shunk sets up along the corresponding Jacobian determinant of the sizable scope phase of phase path point transformation.It is with good conditionsi that the anti-Liouville's theorem of non-Hamilton's mechanical system is set up, and setting up just as Hamilton's mechanical system Liouville's theorem is to have ready conditions equally, but universal significance is separately all arranged separately.

Technical scheme of the present invention is: only need be in two utmost point iron that the anti-Liouville's theorem of non-Hamilton's mechanical system that above-mentioned phase space phase volume is dwindled is set up in the practical application, the corresponding Jacobian determinant of one section phase point transformation of intercepting descends comparatively fast that part of, just can reach the optimal damping effect, such secondary magnet not only can use as guidance magnets; And can or be called strong cooler use as the heavy damping device, emittance is shunk rapidly.Several identical this guidance magnets can be arranged in storage rings according to some cycles, and its minimum period number is five, and does not resemble three in the isochronous cyclotron; Also can rationally form storage rings with four utmost point iron or other concentrating element, beam emittance can be shunk rapidly, improves brightness, realizes that easily line absolutely injects continuously.

Subsequently, utilize several double coolers of doing of identical this guidance magnets, finished the physical Design of heavy damping storage rings,, done the tracking of particle movement and calculated, obtained the damping phasor of emittance fast contraction by Computer Simulation.The result shows that cooldown rate is exceedingly fast Bu Dao the one-period that From rotates, and realizes the hundred-percent continuous injection of line, easily even thoroughly solved unsolved so far this great difficult problem of the mankind, small and exquisite again economic ， And can effectively realize various charged ion nuclear reactions therein.

The present invention has following accompanying drawing.

Fig. 1, be the diagram of the anti-Liouville's theorem heavy damping of non-Hamilton's mechanical system storage rings magnet polar front shape.

Fig. 1 is the diagram of the anti-Liouville's theorem heavy damping of non-Hamilton's mechanical system storage rings magnet polar front shape.In two utmost point iron that the anti-Liouville's theorem of non-Hamilton's mechanical system that the phase space phase volume is dwindled is set up, the corresponding Jacobian determinant of one section phase point transformation of intercepting descends comparatively fast that part of, wherein corresponding equilibrium orbit deflection angle is 2 π/5, and magnet outlet limit is vertical with corresponding equilibrium orbit.The inlet limit of two utmost point iron is parallel with the outlet limit, five double coolers of doing of identical this guidance magnets, form five unit periodic structures, Fig. 1 is five unit periodic structures magnet polar front shapes up and down, vacuum chamber is placed on up and down between the magnet pole-face, charged particle beam is constrained in the vacuum chamber from the successive Zhu Ru of direction shown in arrow And, makes it constantly do shuttling movement, thereby can keep several hrs even longer time.

Computer Simulation has been made in particle movement under this structure.Initial conditions xi=8Cm, xi '=0.0, Xiang Dang Yu From 8Cm outside equilibrium orbit is parallel to equilibrium orbit incident, use the Long Gekuta method, make the double precision track and follow the trail of calculating on the sixteen bit computer, computational accuracy can reach 1 micron, notes down a point mutually every 1 magnetic field structure cycle.The first six point minute Fabric is very irregular, free oscillating period, changed very fast when large amplitude was described, but it is also very fast that amplitude shrinks, when 1 circle back particle is got back to initial azimuth once more, amplitude is retracted to 3.641Cm, illustrate that Xiang Ti Plot contraction is far away from half, cooldown rate is far less than a circle, and this is the electron beam cooling or cools off at random and all can't compare.In addition, the circle spacing surpasses 4Cm, can accomplish that not only 100% injects, and technical easier realization.Amplitude is retracted to below one millimeter after five circles, illustrates that the limit trends towards zero.

Effect of the present invention is: the anti-Liouville's theorem heavy damping of non-Hamilton's mechanical system storage rings, even in permanent electromagnetostatic field, emittance also can be shunk rapidly, compare for the last invention of [00107730.9] with our patent No., line cooldown rate Bu is Dao the one-period of From rotation, the hundred-percent continuous injection of easier realization line, even thoroughly solved unsolved so far this great difficult problem of the mankind, the easier line of making injects the accumulation storage rings continuously.

Its simple economy is easily gone, and only needs to select appropriate parameter when the design storage rings, makes storage rings itself have the heavy damping function.Therefore do not need plus external equipment and additional investment.

Under the condition of non-permanent electromagnetostatic field, above-mentioned self heavy damping function still remains unchanged, thermal insulation cooling of Fa Xianing or synchrotron radiation cooling effect already, and stack obtains better effect simultaneously.Certainly, also can be as required, cooling of affix electronics or cooling more at random, effect all superposes, and therefore has compatibility and Overlay.

The particle beams rotates in storage rings with the speed near the light velocity, and speed is very high, and per second is more than megacycle usually.Inject this great difficult problem continuously even solved the unsolved so far line of the mankind, this just makes the accumulation efficient of line in storage rings improve up to ten thousand times, restraint continuously by the weak current in the injector, change the pulse high-current beam of continuous injection accumulation storage rings rapidly into.This will be after laser, for the mankind seek a new way that obtains high brightness pulse high-current beam.And the electric work conversion efficiency is higher, even can solve the more unsolved so far significant problems of laser.

An application examples of the present invention is the charged ion reactor.

As shown in Figure 1, between two two utmost point iron, do not insert other concentrating elements such as four utmost point iron, facility compact, the anti-Liouville's theorem heavy damping of this small-sized non-Hamilton's mechanical system storage rings, be more suitable for realizing therein various charged ion nuclear reactions, can be described as the charged ion reactor, can effectively realize thermonuclear fusion.

Its operation principle is as follows, by the living beam of charged ions of Jia Su Qi Productivity, for example inject by position shown in the arrow of the outer somewhere of equilibrium orbit, revolve turn around after, when arriving same azimuth once more, be retracted to from equilibrium orbit more nearby, amplitude has reduced mostly, so, beam of charged ions just can be injected near the equilibrium orbit continuously by the outside.For example the deuterium bundle is injected ， And and fill with thin tritium gas at vacuum chamber, tritium Electricity is from forming plasma, and the deuterium bundle is continuous and plasma triton collision at rotary course, and quite deuterium is beaten the tritium PLASMA FOIL.It can make the ionization energy depletion hang down five magnitudes, every circle line subtended angle and amplitude shrink a lot, can effectively offset the expansion that scattering causes, thereby the anti-Productivity of answering is led improve five, six magnitudes, can effectively realize various charged ion nuclear reactions, be the effective new way of simple economy that realizes various thermonuclear fusions such as deuterium tritium, deuterium helium-3, deuterium deuterium, hydrogen boron.

Reference paper

[1]H.Wiedemann，Nucl.Instr.&?Meth.In?Phys.Res.A246(1986)4

[2]E.D.Courant，H.S.Snyder，Ann.Phys.3(1958)1

[3]V.V.Parkhomchuk，A，N.Skrinsky，Reports?on?Preg.In?Phys.Vol.54，No.7(1991)919

[4]D.T.Greenwood，Classical?Dynamics，(1977)P183

Claims (8)

1, the anti-Liouville's theorem heavy damping of a kind of non-Hamilton's mechanical system charged particle storage rings.It is characterized in that utilizing specific guidance magnets, Yun Dong charged particle therein, the inferior lattice that corresponding Lagrange's equation is separated have a zero point than determinant, it faces separating of territory and is not unique, the phase point transformation is not one to one, corresponding Hamilton's equation is interdependent, just undefined, the phase space phase volume is observed the anti-Liouville's theorem of constantly dwindling, certain of particle movement organizes horizontal amplitude of free oscillations and corresponding canonical momentum both constantly trends towards zero, make guidance magnets have both heavy damping or cooling effect fast, several identical this guidance magnets can be arranged in storage rings according to some cycles, also can rationally form storage rings with four utmost point iron or other concentrating element, beam emittance can be shunk rapidly, improve brightness, realize that line injects ， And continuously and can effectively realize various charged ion nuclear reactions therein.

2, storage rings as claimed in claim 1 is characterized in that the charged particle ， Transverse that moves in two utmost point iron does not observe the Liouville's theorem of phase space phase volume conservation to free oscillation, and observe the anti-Liouville's theorem of non-Hamilton's mechanical system that the phase space phase volume is constantly dwindled.

3, as described in the claim 1,2, this-specific guidance magnets in, certain group particle movement track must have a Jian Jin Line, must be elected to be equilibrium orbit to one of them, than determinant arranged so that guarantee the inferior lattice that corresponding Lagrange's equation is separated a zero point, respective transversal amplitude of free oscillations and corresponding canonical momentum both constantly trend towards zero.

4, according to claim 1, it is characterized in that several identical this guidance magnets can be arranged in storage rings according to some cycles, be specifically designed to and effectively realize various charged ion nuclear reactions therein, this special equipment also is called the charged ion reactor, can effectively realize thermonuclear fusion.

5,, it is characterized in that utilizing two utmost point iron that emittance is shunk as described in the claim 1,4.Can be used for offsetting the emittance expansion that scattering and nonlinear resonance etc. cause.

6, as described in the claim 1,4, its domestic animal is characterised in that and utilizes two utmost point iron to make the emittance fast contraction, realizes repeatedly or continuously injecting of line.

7, as described in the claim 1,4, it is characterized in that utilizing two utmost point iron that emittance is shunk, improve beam luminosity, obtain the low emittance bundle of high current.

8, according to claim 1, it is characterized in that all having the heavy damping effect under the condition of or alternating electromagnetic field quiet, both can use separately in perseverance; Again can with other adiabatic cooling, the synchrotron radiation cooling, the electronics cooling or at random cooling wait the stack application.

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