Method of accelerating macroparticles. RU patent 2510603.

FIELD: physics.

SUBSTANCE: in the present method, macroparticles are accelerated by the field of an electromagnetic pulse moving on a helical structure. Power is fed to a helical waveguide and tapped from it on a coaxial cable through wave impedance matchers. The electromagnetic wave is slowed down both owing to geometric properties of the helical structure itself and medium filling, having higher permittivity ε (water, barium titanate), of the region between the helical structure and the shield. The accelerated macroparticles have a cylindrical shape with cylinder diametre d_sh=2 mm, and length of the conical part l_cone=13 mm and overall length of l=300 mm. The cylinders are pre-accelerated to velocity V_in=1 km/s using a gas-dynamic method. The macroparticles are irradiated with a beam of electrons from an electron accelerator. A pulse which accelerates macroparticles in the longitudinal direction is synchronously transmitted into the helical waveguide with injection of macroparticles.

EFFECT: higher rate of gaining energy by macroparticles and creating conditions for macroparticles to penetrate the atmosphere without fatal loss of velocity when the accelerator is placed horizontally.

1 dwg

The invention relates to the field of accelerator physics and can be used to solve scientific and applied problems, in particular, for the creation of artificial stream micrometeorites, removal of debris and in the military.

The technical field

Known [1], the method of acceleration of particles, the spherical form, namely, that the particulates are electrically charged by the contact method and charged particles accelerate the electrostatic field. The energy of particles in it is small and limited to high-voltage potential on the conductor. Actually, the voltage at the conductor may not be significantly more than 3 MV, respectively, these particulates can be used only in a vacuum. In the conditions of earth's atmosphere such particulates will quickly lose its speed due to the air resistance to their movement.

Known [2], the method of acceleration of particles of spherical shape of the spiral waveguide in which: particulate electrically charged, pre-speed electrostatic way to speed corresponding to the speed of injection, and finally speed up running the spiral waveguide an impetus that can be chosen for the prototype.

Disadvantages prototype

However, the well-known method of acceleration of particles of spherical shape with a mass of the order of a few grams suffers from two fundamental shortcoming: the low rate of acceleration and the inability of such particles cross the earth's atmosphere, especially at horizontally located accelerator.

Indeed, spherical mass of particulates grows with the diameter of the ball as the cube diameter. Size of the sphere, which includes excessive charges placed on the ball, grows as the square of the diameter. Therefore, the excessive charges placed on a ball, its weight will decrease with increase in diameter of the sphere. This will lead to the decrease of the parameter Z, where Z is placed on a ball electric charge, And the atomic mass of the ball, and reduce efficiency of acceleration.

In order to better understand the fundamental deficiencies in the acceleration of spherical particles, will prepare comparison Table 1 main parameters of the accelerated balls depending on their diameter for the case of iron balls.

The main parameters of the accelerated spherical particles

D sp , u

Eph, MeV

3.2* 10 -11

3.2*10 -6

1.2*10 -5

3.2*10 -5

3.2*10 -2

1.2*10 -6

In all cases, the tension electric field on the surface of the balls is equal to E surf =10 9 V/cm. In the first column is D sp - ball diameter in microns, and the second column And is the atomic mass of the ball in the atomic mass of the nucleon, the third column is the charge Z, planted on the ball in units of charge electron, in the fourth column, Z/A - extra charge), located on the ball, to its mass, the fifth column potential F. ball - the energy that should have electron to overcome the rejection previously posted on the ball of electrons in the sixth M - mass of the ball in grams, in the seventh β sp - the initial speed of the balls, they gained after acceleration in electrostatic field with a voltage inj U =250 kV, expressed in units of the speed of light: β sp =V sp /c, where c=3*10 5 km/s, the speed of light in vacuum.

A comparison of the data in Table 1 shows that with increase in diameter of balls atomic weight and weight (columns 1, 6) grows as the cube of the radius, as the square of the radius increases needed a charge that must be stored on the ball for achieving the field strength E surf =10 V/cm. Attitude the charge is placed on the ball to his weight (column 4), linearly decreases with increase in diameter, and it means, that with increase in diameter linearly decreases the efficiency of acceleration, i.e. in the field of the same tensions, at one and the same length of the accelerator, balls larger diameter will score a lower rate.

If you go to the acceleration of hollow balls, which almost all mass is concentrated in the shell, then with increasing diameter and surface area, which includes excessive charges, and the mass of particulates will grow quadratically. However quadratic growth diameter will grow and the cross-sectional area particulate spherical form, so that the brake force from the air per unit mass) will remain unchanged.

So hollow particulate spherical especially in comparison with solid particles will not be able to penetrate the earth's atmosphere. It is well known from domestic views, meteor rain is burning up in the atmosphere of the micrometeorites. Physically, this is due to the fact that the coefficient for the bodies of the spherical shape is close to 1, [3], and their speed in the dense layers of the atmosphere decreases rapidly.

The drag coefficient for a sphere, not depending on its diameter and for hypersonic speeds, [3], is almost constant and large, of the order of unity.

For particulate cylindrical shape, with constant cross-section, braking force from the air per unit mass, while increasing the length of the cylinder will decrease.

The empirical formula for the coefficient a sharp cone, [4], quadratic depends on the angle of the solution of a cone with vertex of the angle at the vertex of a cone, this factor can be changed, and at a small angle at the vertex of a cone coefficient aerodynamic resistance can be much less than unity.

The technical objective of this method is to eliminate these shortcomings, that is to increase the tempo set the energy of the particle acceleration of the spiral waveguide and the creation of conditions allowing the macroparticles to penetrate the atmosphere without fatal loss of speed when horizontally located accelerator.

The essence of the invention lies in the fact that this method of acceleration of particles of their pre accelerate to a speed corresponding to the speed of injection into the spiral waveguide the particulates is irradiated with a beam of electrons produced from the electronic accelerator, electrically charging them, and finally accelerate the particulates field of a traveling on one of the spiral waveguide electric pulse and the particulates are cylindrical in shape with sharp cone in the head part corner solution cone Theta≈0.1, with a small asymmetry, leading to the lifting force, With y =2.5*10-2 , so that the coefficients of this model has Since x and lifting force C y approximately equal To x ≈C y and by the absolute value amount value, many smaller units, C x C y - 1.

The distinguishing features communication with positive effect

1. Electrostatic ratio

Compile a comparative Tables 2, 3, which will collect basic parameters of the accelerated particles cylindrical shape, depending on the diameter and length of the cylinder to the same surface of the field strength: E=10 -9 V/cm.

First, find out how dependent placed on a cylindrical segment of electric charge on the diameter of the cylinder. Will prepare comparison Table 2 parameters of interest for a few diameters Explorer with the same length of wire: l=10 mm. The table is compiled for the same surface of the field strength: E=10 9 V/cm.

Comparative parameters of cylindrical particles

Diameter d sh , mu

Eph, MeV

1.5*10 17

2.5*10 -7

3.16*10 -5

1.5*10 19

2.5*10 -5

1.5*10 21

2.5*10 -3

3.16*10 -6

It is visible, that with increase in diameter of the cylinder is linearly decreased very important to accelerate particles parameter Z/A characterizing efficiency of acceleration. The rapidly growing potential of a cylindrical segment, and thus require increasingly high energy electrons to overcome the rejection of the previously placed on a section of the cylinder particles. Therefore, the diameter of the cylinder is necessary to choose the possible small.

Will prepare comparison Table 3 where comparison with spherical objects will hold for objects of cylindrical form with cylinder diameter d=20 microns, for two length values: l=2 mm and l=10 mm. As in Table 1, in all cases, the electric field on the surface of the object is equal to E=10 9 V/cm. In the first column is the length of the 1 - cut in millimeters for the same values of d=20 micron - diameter of the cylinder. The second column shows And nuclear the weight of the cylinder in the atomic mass of the nucleon, the third column is the charge Z, which should be planted on a macro particle to achieve field strength F=10 9 V/cm, expressed in units of electron charge, in the fourth column, Z/A - extra charge), located on the cylinder to its bulk in the fifth column M is the mass of the segment of the cylinder, expressed in grams.

The main parameters of the accelerated particles cylindrical

d sh =20 mu

1.5*10 19

2.5*10 -5

A comparison of the data provided in Table 3, shows that the mass and charge, placed on the cylinder grow linearly with the length. Thus, the parameter Z/A - the ratio of charge to mass not depend on the length of the cylinder unlike particulate spherical form, where this is essential for accelerating the parameter characterizing the efficiency of acceleration, linearly decreased with increase in diameter of the particle. The value of this parameter is large, about the same as for spherical particulate same diameter as the diameter of the cylinder. The mass of particulate cylindrical hundreds of times greater than the mass of particulates spherical shape with a diameter equal to the diameter of the cylinder.

2. Ballistics

Calculate the motion of macroparticles cylindrical shape with sharp cone in the head part with the resistance of the air. The equation of motion of the particle can be written as:

where m is the mass of particulates, V is the velocity, S tr - the cross-sectional area of particulates

- the barometric formula changes of the atmosphere's density with altitude, p 0 =1.3*10 -3 g/cm 3 - air density at the Earth's surface, N 0 =7 km - the value of the height at which the density falls in e times.

Aerodynamic coefficient or the drag coefficient is called a dimensionless quantity, taking into account the "quality" of the form of particulates,

The solution of equation (1) can be written as:

In order to calculate the speed variation particulate over time, it is necessary to find aerodynamic coefficient With x .

3. Calculation of the coefficient of aerodynamic resistance

We assume that the macro particle has the form of a cylindrical rod with conical head part. Then, when you hit the nitrogen molecules in sharp cone, change the longitudinal velocity of the molecules is:

where q t - cone angle at the vertex. Gas molecules transmit the macro particle momentum:

Change pulse per unit of time, the power, the power of the frontal braking,

Dividing F x1

, will get the drag coefficient for a sharp cone with specular reflection of molecules from cone (Newton):

Let the length of a conical part of the particulates equal to: l cone =1.3 cm in diameter d sh =2 mm. This means that the angle at the vertex of a cone is equal to: Theta t =1.6*10 -1 and the drag coefficient for a sharp cone is equal to: x =2.5*10-2 .

The proposed method can be implemented using the device

Figure 1 shows the scheme of the device. The device consists of a gun 1, where cylindrical rods 2 with conical head part are accelerated to the initial velocity V in =I km/s. The rods is irradiated by an electron beam from a special electron accelerator 3. Field of high-voltage current pulse voltage: U acc =2 MV propagating in sections 4 spiral waveguide with a total length L acc =300 metres, cylindrical rods accelerate until the final speed V, fin =6 km/s. Rods focus using doublets electrostatic quadrupole lenses 5, located between sections, and then released into the atmosphere through a sequence buffer volumes 6, having individual pumping 7.

1. The choice of the finite speed of rods

The ratio between the speed and energy per nucleon, it can be seen from the following table.

The dependence between the velocity of the projectile and the energy per nucleon

V sh , km/s

e, eV/nucl.

It is seen that the finite speed of the particulates equal to V sh fin =6 km/s, corresponds to the energy per nucleon in the projectile order fin W ≈0.2 eV/nucleon.

2. Pre-acceleration of particles of gas-dynamic method

Initial, powder after start-up, the speed of the particulates can be estimated from the following considerations. Thermal velocity of the molecules of burnt gunpowder can be determined from the molecular weight of the products of combustion M and temperature burned products T:

where k=1.38*10 -16 erg/degree - Boltzmann constant, lerg=6.24*10 11 eV, M=Nm n , where m n is the mass of the nucleon, m, n c 2 =1 GeV, N is the number of nucleons in the molecules of the products of combustion, N=100, C=3*1010 cm/s, the speed of light in vacuum, T=10 degree. After substituting numerical values in the formula (1), we find that thermal velocity of combustion is equal to: β T =3*10 -6 . While the actual speed of the projectile will be: V sh =1 km/s.

To achieve this speed of the projectile outstretched, arrow-shaped forms, you may need to pump the gun, i.e. removal of gas from the trunk when the shot. The amount of back pressure, pressure acting on the air side, in the trunk, on a projectile can be estimated from the formula:

where p is the density of compressed air gun, p=3 4ρ 0 , p 0 =1.3*10 -3 g/cm 3 - air density under normal conditions. After substituting numerical values in the formula (9) we obtain that the value of backpressure can be: P Orr =2.5*10 7 dn/cm 2 =25 atm. Thus, the pumping out of the barrel of the gun can be very useful. In vacuum same should be done and electrodynamic dostoinye shell, and release it into the atmosphere must be through a sequence of pumped buffer volumes.

Perhaps, however, the use of fin-stabilised discarding sabot projectile will provide higher muzzle velocity than we assume.

3. The acceleration of particles in spiral waveguide

It is known [2]that the spiral waveguide can spread slow electromagnetic wave phase velocity which may be of the order of the speed of sound in air. In such waveguide is possible to accelerate electrically charged rods with conical head part, for this purpose, the initial velocity of the rod and the phase velocity of the wave approximately coincided. As the acceleration of the rod phase velocity of a wave in a spiral waveguide need to increase so that the rod was all the time in the same phase, called synchronous. Increase the phase velocity of a wave in a spiral waveguide can, increasing step winding spiral [2].

Speeding the rod must contain the engine for correction of orbit during a flight in the air, engine fuel. You also need to have the guidance system of a rod on space debris, the rod must contain a navigation system, control system, the transmitter and receiver.

The diameter of the rod may be equal to: d sh =2 mm, length l sh =300 mm.

Then the cross-sectional area of the rod is equal to:

s tr =πd sh 2 /4=3.14*10-2 cm 2 , the volume of rod: V sh-1 cm 3 . The mass of rod, for the case of the average density of the rod p aver =5 g/cm, equal: m sh =5 g.

3.1. The Ratio Z/A

Take the average atomic mass of rod is equal to A sh =30. Find the number of nucleons in the rod out of proportion:

6*10 23 - 30 g

where x=10 23 atoms or A sh =3*10 24 nucleons.

Take a superficial tension of electric field on the rod is equal to: E surf =3*10 7 V/cm. From the formula for the surface tension of the field for the cylinder:

find the charge density per unit length of the rod

whence you can find:

Thus, if "planted" on the rod N e =3*10 14 electrons, the surface tension of the field will be equal: E surf =3*10 7 V/cm.

Now, knowing the total number of excess electrons on the rod N e =3*10 to 14 and the number of nucleons in it A sh =3*10 24 , you can find the ratio of charge to mass for rod: Z/A=N e /A=3*10 14 /3*10 24 =10 -10 .

3.2. The length of the acceleration

Acceleration rate charge in an electric field can be written as:

and the strength of the wave field zw E =70 kV/cm set tempo energy will be: ΔW=7*10-4 eV/(m*nucleon), so that the required increase energy Δε=0.2 eV/nucleon, it has been at length:

what is acceptable for hosting accelerator on the ship.

4. Irradiation of terminal electron beam

In order to speed up the spiral waveguide cylindrical rod with a sharp cone in the head part, it must be electrically recharged. To inform the electrical charge of the terminal is possible, irradiating it with a beam of electrons, so that bombard core electrons, it remained. Then the electric charge of the rod will grow proportionally to the current of the electron beam and duration of exposure. Let the current scanning probe rod electron beam is equal to: I-beam =5 a And the current pulse duration equal to: t beam =10 ľs. Then the total number of electrons in such a current pulse just equals: e N =I-beam *t beam /e=3*10 14 electrons.

4.1. Radiation particles by electron beam. The energy of the electrons

Let quicker gas-dynamic way to speed V in =1 km/s cylindrical rod gets the electron beam is obtained from an external source. We will proceed from the surface of the field strength: E surf =30 MV/cm. Then for cylinder diameter d sh =2 mm will provide that the minimum energy of electrons that can overcome the Coulomb repulsion previously posted on the macro particle electron should be: W e >eE surf *d sh /2=3 MeV.

4.2. Radiation particles by electron beam. Landing run

The electrons with energy of 3 MeV has mileage in aluminium is approximately 1 g/cm 2 , [5], str. Taking the density of aluminum equal to: p A1 =2.7 g/cm 3 , we find that the extrapolated path of the electron in aluminium equal to: l A1 ≈4 mm. Since the average density of the matter, we have chosen for the cylinder, p aver. =5 g/cm 3 , about twice the density of aluminum, the mean free path of electrons with an energy of 3 MeV in the terminal will be about the same: 2 mm.

Apparently, should gradually increase energy electron irradiation process. Need, to as "placement" of the electrons at the core of the electrons emitted later, on the one hand was big enough energy to overcome the Coulomb repulsion in the core electrons, on the other hand, the energy of the electrons should not be too large - it is necessary to run electrons in matter rod was much less than its diameter.

In this energy range, the mileage of electrons in matter grows linearly with energy, for example, electrons with energies W e =300 keV, has mileage 0.2 mm and will not be able to cross the diameter particulate 2 mm. They will lose their energy for ionization of matter and will stay in the thickness of the particulates.

4.3. Radiation particles by electron beam. Autoelectronic emission

"Plant" number of charges on the macro particle - 't be a problem, but then, when electrons macro particle will be much, they will start to drain from it at the expense of field emission. Let the intensity of the field to field emission is: E surf =3*10 7 V/cm. Once planted a lot of electrons, in order to plant next, we need to overcome the rejection of those already there. And this means that the energy of the electrons, we want to plant a macro particle must be large enough such that they could overcome the Coulomb barrier, fly to the particulates and for her to remain.

"Plant" large electrical charge will interfere autoelectronic emission. The part of the charge by the tunneling effect will continue to flow with the particulates.

4.4. Coating cylinder platinum and oxygen passivation

To create a surface barrier for electrons, "set" on the macro particle, may need more work function of electrons from the particulates. The most famous work output has platinum, passivated oxygen, φ=6.56 eV, [5], str. Posted on the macro particle charge will be with her to flow through the field emission in accordance with the formula [5], str.

where q(y) is a function of Nordheim in which argument is a relative decrease of output for external electric field on Schottky.

4.5. The electron leakage

Find the number of electrons leaving the macro particle, during acceleration. For field strength: E=30 MV/cm and work output: φ=6.5 eV from the graph, [5], CTR, we find that the density of the leakage current is: j=10 -9 A/cm 2 .

Leak charge ΔQ will be:

where j=10 -9 A/cm 2 - leakage current, S surf ≈20 cm 2 - area of the lateral surface of the particulates.

Acceleration can be determined from the relation:

where L acc =300 m is the length of the acceleration, V aver =3 km/s the average velocity of the length of the acceleration. Calculated by the formula (17) acceleration is equal to: t acc =0.1 s.

Putting the numbers in the formula (16), we find that ΔN e =10 electrons and this is 3*10 -5 from the number of electrons planted on the macro particle.

5. The choice of the parameters of the spiral waveguide

Initial speed in a spiral β sh in , expressed in units of the speed of light β in =V-in /C, where C=3*1010 cm/s, the speed of light in vacuum is equal to: β in =3.3*10-6 , final: β fin =2*10 -5 . Spiral, presumably, will consist of several sections, so that within each section you can select an optimum rate of acceleration. Wavelength acceleration can be determined from the condition: x=2πr 0 /(?*λ 0 )=1, where x is the dimensionless parameter included in the arguments of modified Bessel functions, r 0 is the radius of the spiral, beta - phase velocity of the waves, light wavelength 0 - wavelength acceleration in vacuum, light wavelength 0 =c/f 0 , f 0 - frequency acceleration.

Choosing the initial radius of the spiral r 0 in equal: r 0 in =20 cm, ε=1280 - dielectric permeability of the environment, located in the area between the coil and the screen will find; 1 0 =3.8*10 7 cm, f 0 =790 Hz. Thus, a slow wavelength for the beginning of acceleration equal; 1 slow =βλ 0 =1.25 m.

5.2. The parameters of the spiral

In order to obtain the desired field strength of wave E 0 the spiral waveguide, it is necessary to enter the power is determined by the formula. [2]

where P is entered into the spiral waveguide high-frequency output, r 0 is the radius of the spiral, beta - phase velocity of the wave is determined from the dispersion equation. Curly bracket in the formula (1) is equal to:

where I 0 I 1 , I 2 - modified Bessel functions of the first kind,

To 0 , K 1 , K 2 modified Bessel functions of the second kind. The first term in curly brace corresponds to stream extending inside the spiral, the first term corresponds to the stream extending out of the spiral. Since the space between the coil and the screen filled with a dielectric, before the second summand appeared cofactor e, [2].

In our case, the delay of electromagnetic waves to the speeds of the order of the speed of sound you want to use as the geometric properties of the structure (spiral with fine pitch), and the physical environment, we have chosen a value of relative permittivity ε=1280.

Thus, the flow of high-frequency power, spreading outside spiral, more than 10 times exceeds the capacity, propagating inside a spiral. Therefore, the first item inside the braces can be neglected compared with the second, the value braces for the argument x=1 is approximately equal to: {}≈4ε.

In accelerators synchronous phase select on the front slope of the pulse, so accelerating particle electric field always less than the peak value. Select synchronous phase is equal to: & Phi; s =45, sinφ s =0.7, zw E =E 0 sinφ s . Thus, the amplitude of the wave, which will accelerate cylindrical rod, must be equal to:

Then wave power is expressed by the formula (18) in Watts equal to:

5.2. The transition from a sine wave, single pulse

Such power may be achievable for pulse technique. Lay-sine pulse, [2]corresponding to the E-wave pulse =E 0puise sin(0.67 T/T 0 )t 0.67/T 0 =ω 0 , ω 0 =2πf 0 in the Fourier series.

Range of impulse rather narrow and covers the frequency range from 0 to 2ω 0 . Since the spiral waveguide dispersion dependence of phase velocity of frequency) is weak, it can be expected that the full range of frequencies from 0 to 2ω 0 will be distributed approximately the same phase speed. In the half-wave sine wave pulse in space will grow 3.5 times only by increasing the phase velocity of the wave. Approval of the spiral waveguide with feed feeder in this case should be implemented in the frequency band: F≈ω 0 /0.67.

We introduce the notion of amplitude pulse U-related field intensity in the axis of the spiral E 0 value, [2]:

The choice of the wavelength λ 0 =3.8*10 7 cm means that we have chosen the length accelerating the magnetic dipole momentum is equal to: (f 0 =/λ 0 =790 Hz), pulse t =1/(2f 0 )=630 ľs. The amplitude of the voltage pulse will be:

and pulse current in coils of the spiral will be:

. Table 5 includes main parameters of the accelerator.

The parameters of the accelerator

Z/A=10 -1010 , dielectric outside spiral, wave power, R.

P=300 MW u=1, ε=1280

Speed, initial - end,? ph

β ph =3.3*10 -6 -2*10 -5

The initial radius of the spiral, r 0

r 0 =20 cm

The wave frequency, f 0 ,

f 0 =790 Hz

The electric field E 0

E 0 =100 kV/cm

The length of the accelerator, L acc

L acc =300 m

Pulse duration, t

t=630 NTU

The amplitude of the voltage,

Current amplitude

5.3. Attenuation capacity at the distribution of the pulse spiral

The wave attenuation in the spiral waveguide will be to cause the amplitude of propagating along the spiral pulse will diminish as the movement of the pulse from the beginning to the end of the spiral, and this decrease is connected with resistive currents going on heating spirals.

Current ij flows through the coils of the spiral and actually ohmic losses it

where ij - current in a coil in Amperes, R - coil resistance in ohms. Then Δ/revolution - will be expressed in Watts.

Find first resistance coils. The resistance is calculated by the usual formula: R=ρl/s, where p=1.7*10 -6 Ohm*cm - specific resistance of copper, we assume round copper, l=2πr 0 - turn length, r 0 is the radius of the spiral, s is the cross section of a loop. Since the current in a spiral, high-frequency (AC), appeared the factor 1/2 and such current penetrates conductor on the depth of the skin layer, which must be found.

The expression for the depth of the skin layer can be written as:

& Radic;

where C=3*1010 cm/s is the speed of light in vacuum, σ=5.4*10 17 l/s is the conductivity of copper, ω 0 =2πf 0 - circular frequency, f 0 =790 Hz - frequency wave propagating in a spiral. Substituting numerical values into the formula (25) is: m=0.24 cm.

The calculations performed in [2] for the exact formulas show that spiral radius of 10 cm and the phase velocity β ph =10 -5 number of spiral turns per inch is equal to n=50. With increase in the radius of the spiral in 2 times in comparison with the value considered in [2], and the reduction of the phase velocity of 3 times the number of turns per inch, will increase in 1,5 times and will amount to begin the spiral: n=75.

Turned out the depth of the skin layer, m=0.24 cm, far larger than the distance between the turns of the spiral h=l/n=0.013 cm, where n≈75 - number of turns of the spiral, per 1 cm of length of the spiral. This means that to reduce the resistance of one turn and accordingly to reduce damping-wound spiral have quite a wide band width: N=2?=0.5 cm. The tape should be placed wide Mr radius, spaced, for example, h/2, so that from step winding h-size, h/2 took a turn, and the space h/2 was equal to the gap between the coils.

The resistance same orbit R=ρl/s is:

The numerical value for the beginning of the spiral r 0 =20 cm, find

Now we find ij - current in coils. To do this, use the formula:

where H zsurf - magnetic field on the surface of the spiral.

Find the link between the component of the electric field E 0 on the axis of the spiral and the magnetic field component Hz to spiral surface: H zsurf =(k 1 /k)tgΨI 0 (k 1 r 0 )E 0 I 0 (k 1 r/I 1 (k 1 r 0 ), [2]. For the inner region of the spiral, where k 1 - transverse wave vector k=(W/c)*ε 1/2 - wave vector, r 0 is the radius of the spiral, the expression is: (k 1 /k)=1/β ph , tgΨ≈h/2πr 0 , so that for k 1 /k)*tgΨ=ε 1/2 . For k r 1 0 =1 ratio of I 0 (k 1 r 0 )/I 1 (k 1 r 0 )=2.

Thus, the component of the electric field: E 0 ≈100 kV/cm on the helical axis corresponds to the magnetic field strength H zsurf =25 kGs in a spiral surface.

Now you can find current in coils of the spiral, the Current nI Phi can be found from the relation: nI j (A/cm)=H zsurf /(e/s)=(1.226) -1 *H zsurf (A/cm)=H zsurf (Gs). And, thus, the current in a single turn is equal to:

this is the length at which the field strength is reduced in e times due to attenuation. It is seen that the motion of the particulates when accelerating we should expect taking into account attenuation power of the pulse during the distribution of power in a spiral waveguide.

5.4. The capture of particles in a mode of acceleration. Tolerance

Calculate the required accuracy of coincidence of the initial accelerating the object wave phase (pulse) with simultaneous phase. The capture theory of particles in the running wave gives, [6]: Δφ=3φ s , (+Phi s-2φ s ). Actually this means, for example, that in our case, where T/4 duration corresponds 316 ľs or 90, that one degree phase approximately corresponds to a time period of 3 ľs. In the linear accelerators of the anomaly is giving phase width clot + - 15, and to not have a large phase fluctuations, let us require that the timing accuracy of particulates with accelerating momentum was: Δτ= + 15*3 ľs= + 45 ľs. Such precision synchronization, apparently, are achievable for powder start - pre-gas-dynamic acceleration particles.

Let us calculate now tolerance accuracy of concurrence of initial speed of particulates and the phase velocity of propagating along the spiral structure of the pulse. Enter the value of g=(p-p s/p s - relative difference pulses, [6]. In nonrelativistic case is simply the relative velocity dispersion g=(V-V s/V s . Vertical span separatrix is calculated by the formula [6]:

where: & Phi; s =45°=PI/4, ctgφ s =1, [1-s & Phi; /ctgφ s ] 1/2 =0.46, 2*0.46=0.9 W 1 =(Z/A)eE λ 0 0 sinφs/Mc 2 .

Let us define a value: W 1 =(Z/A)eE λ 0 0 sinφs/Mc - relative set of energy by macro particle at a wavelength of λ 0 in a vacuum. In our case; 1 0 =c/f 0 =3.8*10 7 cm, sinφ s =0.7, Mc 2 =1 GeV, W 1 =2.66*10-6 . Numerical values, we get: g=(V in-V s/V s =ΔV/V s and, finally, ΔV/V s = + [2.66*10 -6 /(6.28*3.3*10 -6 )] 1/2 *0.9= + 0.11.

Thus, the allowable discrepancy initial speed of particulates with the speed of the pulse equals about: ΔV/V s = + 11%. For the initial velocity of the particulates V in =1 km/s tolerance for deviation rate is ΔV<100 m/s.

6. Radial movement

As is known [6], in azimuthally symmetric wave region of the phase stability, the field of autofailure, corresponds to the radial defocusing. In this case, you cannot get a simultaneously acting radial and phase stability, under the conditions of autofailure for radial focusing require external field. In this field phase of the radial component of the electric field of the wave is directed towards increasing radius, i.e. accelerates the particulates by radius.

In this area of the velocities of the particles, hypersonic, hundreds of thousands of times smaller than the speed of light, focusing magnetic quadrupole lenses ineffective, here are the most convenient focusing electrostatic quadrupole lenses. These lenses focus the particle in one plane and defocusing in another. Collected in doublet these two lenses are the result of the focusing effect. The whole accelerator is divided into separate sections, focusing particulate doublets have between accelerating sections. In the work [2], for a focusing of particles with close speeds used doublets with parameters: length lenses l 1 =7.5 cm, length of the gap between the lenses l p =5 cm, so that the total length of the doublet = l d =20 cm

When the acceleration rate of the macroparticles of order E 0m =20 kV/cm) electric field gradients in doublets were about G 1,2m =10 kV/cm 2 . It is seen that doublets electrostatic quadrupole lenses do not greatly increase the length of the accelerator and the electric field strength in them, for distances of the order of 1 cm, should be in the order of intensity of a field in a spiral.

Possible application in military Affairs

1. Loss speed when passing through the atmosphere

Having accelerator such length L acc =300 m, it is necessary to remember, that this length is added to the length of focusing intervals, located between sections, the length of the barrel of a gun, which creates pre-acceleration projectile length release shell exploded in the atmosphere, etc. Apparently, it is advisable to position the accelerator horizontally, on the deck of the ship.

This means that the projectile should have asymmetry generating lift force coefficient C y , and the projectile will lose some speed when lifting to a height where the air resistance can be neglected.

Let the shell with a total length l sh =300 mm has cone length l cone =13 mm in the head part. Then the angle at the vertex of a cone is equal to: Theta cone =d sh /l cone =1.6*10 -1 , and the drag coefficient

Make the table where we the time dependence of the vertical velocity of the magnetic dipole his height and horizontal speed. Vertical speed will be calculated by the formula:

Set height:

- the average vertical speed in the time interval Dt.

The decrease of the horizontal velocity over time will be described by the formula:

The change in air density with height will be considered by the barometric formula: p=p 0 *exp[-y/N 0 ], where H 0 =7 km. Table 6 lists the parameters of flight cylinder depending on time. In the second column shows the vertical velocity of the cylinder, and in the third horizontal velocity of the cylinder, 4 - dialed a height that he would have after appropriate seconds of flight, the fifth - the density of the atmosphere at this altitude.

The flight parameters, for the case of x , C, y =2.5*10 -2

V x , km/s

p air , g/cm 3

1.3*10 -3

Lifting time to the maximum height in this case is:

t max =V y /g=367s, where g=10 -2 km/s 2 is the acceleration of gravity, flight range: S=V x *2τ max =2700 km, maximum altitude stroke: Y=V 2 y /2g=670 km. Changing the shell cone shape in the head part, apparently, it will be possible to move from an abusive shooting for hinged (Zenith) shooting.

The implementation of the invention. Device operation

The device works as follows. Inside the barrel of the gun 1 cylindrical rod 2 with a sharp cone in the head part are accelerated to the speed corresponding to the speed of injection in the spiral waveguide: V in =1 km/s. From a linear accelerator 3 pin exposed to a beam of electrons with energy E=3 MeV, the total number of electrons, planted on rod, N is e =3*10 14 will get the electric field on the surface of the cylinder F=3*10 7 V/cm, the potential of the cylinder: f=3 MeV, the excessive charge to mass Z/A=10 -10 . Field of high-voltage current pulse voltage:

, which sections 4 spiral waveguide with a total length L acc =300 metres, the particulates accelerate until the final speed V, fin =6 km/s. Located between sections of the doublets electrostatic quadrupole lenses 5 particulate focus in the transverse direction. The particulates are released into the atmosphere through a sequence buffer volumes 6, having individual pumping 7.

Conclusions

Maximum lifting height of macroparticles, Y=670 km, better trajectories of missiles and the most part of the satellites.

Firing range, S max =2700 km, is that of the destroyer, located in the Gulf of Aden, you can sweep the whole Bay.

Literature

1. Aigerim. Space materials science. Methodical and tutorial. 2007, Moscow, SINP MSU, s.

2. Sngos, CaseSensitive. About electrodynamic acceleration of macroscopic particles. Message JINR, P9-2009-110, Dubna, 2009, http://www1.jinr.ru/Preprints/2009/110%28P9-2009-110%29.pdf

3. http://dic.academic.ru/dic.nsf/bse/130514/Sverhsvetovoy

4. http://www.oocities.org/igor_suslov/AeroSidelnikov.pdf

5. Tables of physical quantities. Handbook Ed. Ikkicon. Moscow, Atomizdat, 1976.

6. Imoptence. Dynamics of particles in linear resonant accelerators. Moscow, Atomizdat, 1966.

The method of accelerated particles, namely, that the particulates pre accelerate up to speed the corresponding speed injection into the spiral waveguide, the particulates is irradiated with a beam of electrons produced from the electronic accelerator, electrically charging them, and finally accelerate the particulates field of a traveling on one of the spiral waveguide electrical pulse, wherein the particulates are cylindrical in shape with sharp cone in the head part, the angle of the solution of a cone Theta≈0.1, with a small asymmetry, leading to the lifting force, C, y =2.5*10-2 , so that the coefficients of this model has C x and lifting force C y is approximately equal to C x ≈C y and the absolute value amount value, many smaller units, C x C y <<1.