Abstract:
A device including two plasma generation electrodes, a series resonator having a resonant frequency above 1 MHz and including a capacitor with two terminals, and an induction coil surrounded by a screen, the capacitor and the coil being placed in series, the electrodes being connected to the respective terminals of the capacitor. The ratio of the spark plug to the radius of the screen is equal to 0.56. The device can optimize the Q-factor of such a device by adjusting the radius of the coil to that of the screen.

Description:
BACKGROUND 
     The present invention relates in general to the generation of plasma in a gas, and more specifically to plasma generating devices with inbuilt inductance. Plasma generation is used in particular for the controlled ignition of internal combustion engines by the electrodes of a spark plug, but can also be used, for example, for sterilization in an air-conditioning method or pollution reduction systems. 
     More specifically, the invention relates to a plasma generating device comprising two electrodes, a series resonator with a resonant frequency higher than 1 MHz and comprising a capacitor equipped with two terminals and an inductive coil surrounded by a shield, the capacitor and the coil being arranged in series, the electrodes being connected to the respective terminals of the capacitor. 
     A device such as this is described in particular in the form of a spark plug in document FR 2 859 830. This type of spark plug exhibits low internal parasitic capacitances and forms a series resonator that has a high Q-factor. Although this device is able to sustain a radiofrequency voltage between its electrodes to generate a plasma, optimizing it has hitherto remained problematic. 
     BRIEF SUMMARY 
     This being the case, it is an object of the invention to propose a radiofrequency plasma generating device that performs even better. 
     To this end, the device of the present invention, in other respects in accordance with the definition thereof given in the above preamble, is essentially characterized in that the ratio of the radius of the coil r int  to the radius of the shield r ext  is between 0.5 and 0.6 and preferably equal to 0.56. 
     Further specifics and advantages of the invention will become clearly apparent from reading the following description which is given by way of nonlimiting example and from studying the figures. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a sectioned schematic depiction of one example of a spark plug that can be used in the plasma generating system; and 
         FIG. 2  is a graph depicting a study of the Q-factor (y) as a function of the r int /r ext  ratio (x). 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  illustrates details of the structure of a radiofrequency plasma generating device of the prior art, in the form of a surface-spark spark plug for which application of a radiofrequency excitation proves to be particularly advantageous. 
     The spark plug  110  may be fixed to the cylinder head  104  of an internal combustion engine  105  of a motor vehicle. 
     The surface-effect spark plug  110  comprises a low-voltage cylindrical electrode which acts as a metal shell  103  intended to be screwed into a recess made in the cylinder head of an engine and which opens to the inside of the combustion chamber. The shell  103  is intended to be electrically connected to ground. Thus, the shell  103  surrounds a cylindrical high-voltage electrode  106  positioned centrally. 
     The electrode  106  is insulated from the shell  103  by an insulating sleeve  100 . The insulating sleeve is made of a material the relative permittivity of which is greater than 1, for example a ceramic. The spark plug has a gap  105  separating the dielectric  100  from one end of the electrode  103 . 
     For applications to automotive ignition, a person skilled in the art will use electrodes and an insulator that are of materials and of geometries suited to initiating combustion in a mixture at a combustion density and to resist the plasma thus formed. 
       FIG. 1  also depicts a sectioned view of a spark plug advantageously incorporating a series resonator like the one described in the abovementioned prior art document. The spark plug  110  has a connection terminal  131  connected to a first end of an inductive coil  112 . The second end of the inductive coil  112  is connected to an internal end of the high-voltage electrode  106 . This end is also in contact with an insulating element  111  that makes up the capacitor. 
     The electrodes  103  and  106  in this example are separated by the dielectric material  100 . The series resonator incorporated into the spark plug  110  comprises the inductive coil  112  and the insulating element  100  that also forms the capacitor between the electrodes  103  and  106 . The capacitor and the inductive coil  112  are arranged in series. The series capacitance of the series resonator is formed of the capacitor and of the internal parasitic capacitances of the spark plug. This capacitance is arranged in series with an inductor to form the series resonator. When the length of the connection between the inductor and the capacitor is short, the parasitic capacitances in the spark plug are reduced. The spark plug  110  is thus used to sustain the AC voltage between the electrodes  103  and  106  in the desired frequency range, preferably from 1 MHz to 20 MHz. 
     The series resonator incorporated into the spark plug preferably has a single inductive coil  112 , making such a spark plug easier to manufacture. 
     A high number of turns in the single coil  112  is needed to obtain an inductance of the order of 50 μH. Now, a high number of turns generates parasitic capacitances. The single inductive coil  112  preferably has an axis (identified by the chain line) and is made up of a plurality of turns superposed along its axis. It will thus be appreciated that the projection of one turn is the same as the projection of all the turns along this axis. The parasitic capacitances can therefore be limited by not superposing the turns radially. 
     The spark plug also advantageously comprises a shield  132  connected to ground and surrounding the inductive coil  112 . The field lines are thus closed on themselves inside the shield  132 . The shield  132  thus reduces the parasitic electromagnetic emissions of the spark plug  110 . The coil  112  can actually generate intense electromagnetic fields with the radiofrequency excitation that is intended to be applied between the electrodes. These fields may, in particular, disrupt systems carried on board a vehicle or exceed the threshold levels defined in emission standards. The shield  132  is preferably made of a non-ferrous metal with high conductivity, such as copper or silver. In particular it is possible to use a conductive loop as a shield  132 . 
     The coil  112  and the shield  132  are preferably separated by an insulating sleeve  133  made of a suitable dielectric material, with a dielectric coefficient greater than 1, and preferably a good dielectric strength in order further to reduce the risk of breakdown or corona discharge, which cause energy to be dissipated. Of course, the lower the dissipation of energy, the higher the amplitude of the voltage applied between the electrodes and the longer the life of the spark plug. The dielectric material may, for example, be one of the silicone resins marketed under the references Elastosil M4601, Elastosil RTV-2 or Elastosil RT622 (the latter having a withstand voltage of 20 kV/mm and a dielectric constant of 2.8). Provision may be made for the exterior surface of the sleeve  133  to be metalized in order to form the aforementioned shield  132 . 
     In general, preference will be given to a winding of the coil  112  about a solid element  134  made of a material that is insulating and/or nonmagnetic, preferably both. This then further reduces the risks of breakdown and the parasitic capacitances. 
     A plasma formed using such a device has numerous advantages in the context of automotive ignition, including an appreciable reduction in the rate of misfires in a stratified lean-burn system, reduction in electrode wear, or the tailoring of the ignition initiation volume to suit the density. 
     Radiofrequency excitation is also suited to a plasma deposition application, in a gas that has a density of between 10 −2  mol/l and 5×10 31 2  mol/l. The gas used in this application typically may be nitrogen or air, ambient air in particular. 
     Radiofrequency excitation is further suited to an application of reducing the pollution of a gas of a density of between 10 31 2  mol/l and 5×10 31  mol/l. 
     Radiofrequency excitation is also suited to a lighting application calling upon a gas with a molar density of between 0.2 mol/l and 1 mol/l. 
     According to the present invention, in order to optimize the Q-factor Q=Lw/R, it is necessary to determine L, that represents the inductance, and R that represents the resistance. To do that, a long coil model with rectangular turns has been adopted. 
     The current that flows through the wires of the coil  112  will be spread between the interior surface and the exterior surface of the wires in that ratio of the magnetic fields. If the coil is considered to be long enough, and thanks to the presence of the shield, the magnetic field in the coil support and in the space between the coil and the shield is uniform. The flux in the space between the coil and the shield is therefore substantially equal to the flux in the coil support, and the magnetic fields are therefore in the ratios of the cross sections, which gives:
 
 B   ext   =B   int   ×r   2   int /( r   2   ext   −r   2   int )
 
where r int  is the radius of the coil, r ext  is the radius of the shield, B int  is the magnetic field in the coil and B ext  is the magnetic field between the coil and the shield.
 
     By accepting that the distribution of current is entirely dependent on surface area, application of Navier-Stokes to μ 0 B to a square circuit of a width equal to the pitch crossing the surface gives:
 
 I   ext   =B   ext /(μ 0 ×pitch) and  I   int   =B   int /(μ 0 ×pitch)
 
by setting
 
 I=I   int   +I   ext  and  x=r   int   /r   ext  
 
we get
 
 I   int   /I= 1 −x   2  and  I   ext   /I=x   2  
 
where I represents the electrical current, I ext  represents the electrical current in the shield and I int  represents the electrical current in the coil.
 
     The variable x which represents the ratio of the radius of the coil to the radius of the shield can thus be expressed and it is necessary now to express R and L as a function of x so as to find a value of x that maximizes Q=Lw/R. 
     The losses energy balance gives: 
               RI   e     =     ρ   ⁢       n   ⁢           ⁢   2   ⁢   π       δ   ·   pitch       ⁢     (         r   int     ⁡     (       I   ext   2     +     I   int   2       )       +       r   ext     ⁢     I   ext   2         )             
i.e.:
 
     
       
         
           
             R 
             = 
             
               ρ 
               ⁢ 
               
                 
                   n 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   2 
                   ⁢ 
                   π 
                 
                 
                   δ 
                   · 
                   pitch 
                 
               
               ⁢ 
               
                 
                   r 
                   ext 
                 
                 ⁡ 
                 
                   ( 
                   
                     
                       2 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         x 
                         4 
                       
                     
                     + 
                     
                       x 
                       3 
                     
                     - 
                     
                       2 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         x 
                         2 
                       
                     
                     + 
                     1 
                   
                   ) 
                 
               
             
           
         
       
     
     In addition, the inductance L can be calculated as follows: 
     
       
         
           
             LI 
             = 
             
               
                 
                   nB 
                   int 
                 
                 ⁢ 
                 π 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   r 
                   int 
                   2 
                 
               
               = 
               
                 
                   
                     μ 
                     0 
                   
                   ⁢ 
                   n 
                   ⁢ 
                   
                     
                       I 
                       int 
                     
                     pitch 
                   
                   ⁢ 
                   π 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     r 
                     int 
                     2 
                   
                 
                 = 
                 
                   
                     μ 
                     0 
                   
                   ⁢ 
                   n 
                   ⁢ 
                   
                     
                       I 
                       ⁡ 
                       
                         ( 
                         
                           1 
                           - 
                           
                             x 
                             2 
                           
                         
                         ) 
                       
                     
                     pitch 
                   
                   ⁢ 
                   π 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     r 
                     int 
                     2 
                   
                 
               
             
           
         
       
     
     Thus the quality factor is equal to: 
     
       
         
           
             Q 
             = 
             
               
                 Lw 
                 R 
               
               = 
               
                 
                   
                     
                       μ 
                       0 
                     
                     ⁢ 
                     δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     ω 
                   
                   
                     2 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     ρ 
                   
                 
                 ⁢ 
                 
                   r 
                   ext 
                 
                 ⁢ 
                 
                   
                     x 
                     ⁡ 
                     
                       ( 
                       
                         1 
                         - 
                         
                           x 
                           2 
                         
                       
                       ) 
                     
                   
                   
                     ( 
                     
                       
                         2 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           x 
                           4 
                         
                       
                       + 
                       
                         x 
                         3 
                       
                       - 
                       
                         2 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           x 
                           2 
                         
                       
                       + 
                       1 
                     
                     ) 
                   
                 
               
             
           
         
       
     
     In the knowledge that 
               δ   =         2   ⁢           ⁢   ρ         μ   0     ⁢   ω           ,         
it can be deduced that:
 
     
       
         
           
             Q 
             = 
             
               
                 Lw 
                 R 
               
               = 
               
                 
                   
                     r 
                     ext 
                   
                   δ 
                 
                 ⁢ 
                 
                   
                     x 
                     ⁡ 
                     
                       ( 
                       
                         1 
                         - 
                         
                           x 
                           2 
                         
                       
                       ) 
                     
                   
                   
                     ( 
                     
                       
                         2 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           x 
                           4 
                         
                       
                       + 
                       
                         x 
                         3 
                       
                       - 
                       
                         2 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           x 
                           2 
                         
                       
                       + 
                       1 
                     
                     ) 
                   
                 
               
             
           
         
       
     
     Thus, by setting 
               y   =       x   ⁡     (     1   -     x   2       )           2   ⁢           ⁢     x   4       +     x   3     -     2   ⁢           ⁢     x   2       +   1         ,         
a study of this function gives the graph depicted in  FIG. 2  and makes it possible to establish that the maximum in the polynomial fraction lies at y=0.516 for x=0.56.
 
     Thus, in conclusion, it is apparent from this calculation that the ratio of the coil radius to the shield radius needs to be 0.56 in order to have the maximum Q-factor. 
     However, having carried out tests and as shown by the curve, it would appear that a ratio of coil radius to shield radius lying in a range from 0.5 to 0.6 yields highly satisfactory results, allowing a considerable improvement in the Q-factor. 
     This parameter thus allows any type of radiofrequency plasma generating device, for example an engine spark plug, to optimize its Q-factor. 
     It is important to point out that applying such a range of ratio between the diameter of a coil and of a shield can, according to one preferred embodiment, be applied to an engine spark plug but can also be applied to any radiofrequency plasma generating device.