Dielectric electrode assembly and method of manufacture thereof

1. A method of manufacture of a dielectric electrode assembly comprising:

providing a dielectric tube having a cylindrical cross-section and a relative dielectric constant, ε 2 , the dielectric tube filled with a gas having a relative dielectric constant, ε 1 ;

surrounding the dielectric tube with a structural dielectric having a relative dielectric constant, ε 3 ;

positioning metal electrodes on opposite sides of the structural dielectric, the metal electrodes having a flat cross-sectional geometry; and

selecting a material for the structural dielectric such that the relative dielectric constants of the structural dielectric, the dielectric tube, and the gas are interrelated and a uniform electric field is generated within the dielectric tube when power is applied to the metal electrodes.

2. The method as claimed in claim 1 wherein selecting the material for the structural dielectric includes:

selecting R 1 as an inside radius of the dielectric tube and R 2 as an outside radius of the dielectric tube; and

selecting the material for the structural dielectric and the dielectric tube such that the relative dielectric constant of the gas, ε 1 , the relative dielectric constant of the dielectric tube, ε 2 , and the relative dielectric constant of the structural dielectric, ε 3 , are related by a cylindrical tube assembly equation of:

ɛ

3

=

ɛ

2

⁡

[

R

1

2

⁡

(

ɛ

1

-

ɛ

2

)

+

R

2

2

⁡

(

ɛ

1

+

ɛ

2

)

R

1

2

⁡

(

ɛ

2

-

ɛ

1

)

+

R

2

2

⁡

(

ɛ

1

+

ɛ

2

)

]

.

3. The method as claimed in claim 1 wherein positioning the metal electrodes includes positioning the metal electrodes having an electrode width at least one dielectric tube diameter past an edge of the dielectric tube on the structural dielectric.

4. The method as claimed in claim 1 wherein positioning the metal electrodes includes positioning the metal electrodes in direct contact with the dielectric tube.

5. The method as claimed in claim 1 wherein positioning the metal electrodes includes positioning the metal electrodes on the structural dielectric and spaced away from the dielectric tube.

6. A method of manufacture of a dielectric electrode assembly comprising:

providing a dielectric tube having an elliptical cross-section and a relative dielectric constant, ε 2 , the dielectric tube filled with a gas having a relative dielectric constant, ε 1 ;

surrounding the dielectric tube with a structural dielectric having a relative dielectric constant, ε 3 ;

positioning metal electrodes on opposite sides of the structural dielectric, the metal electrodes having a flat cross-sectional geometry; and

selecting a material for the structural dielectric such that the relative dielectric constants of the structural dielectric, the dielectric tube, and the gas are interrelated and a uniform electric field is generated within the dielectric tube when power is applied to the metal electrodes.

7. The method as claimed in claim 6 wherein selecting the material for the structural dielectric includes:

selecting an interior surface of the dielectric tube comprising a semi-major axis dimension, A 1 , and semi-minor axis dimension, B 1 ;

selecting an exterior surface of the dielectric tube comprising a semi-major axis dimension, A 2 and semi-minor axis dimension, B 2 ;

selecting the gas such that the relative dielectric constant of the gas, ε 1 , has a value of 1; and

selecting the material for the structural dielectric and a material of the dielectric tube such that the relative dielectric constant of the dielectric tube, ε 2 , and the relative dielectric constant of the structural dielectric, ε 3 , are related by an elliptical tube assembly equation of:

ɛ

3

=

ɛ

2

⁢

B

2

A

2

⁡

[

A

2

⁢

A

1

2

-

A

1

⁢

B

1

⁢

B

2

+

(

A

1

⁢

B

1

⁢

B

2

-

A

2

⁢

B

1

2

)

⁢

ɛ

2

B

2

⁢

A

1

2

-

A

1

⁢

B

1

⁢

A

2

+

(

A

1

⁢

B

1

⁢

A

2

-

B

2

⁢

B

1

2

)

⁢

ɛ

2

]

.

8. The method as claimed in claim 7 further comprising:

providing another dielectric tube having a cylindrical cross-section and a relative dielectric constant, ε 2 , the another dielectric tube filled with another gas having a relative dielectric constant, ε 1 ; and

selecting a second material for the another dielectric tube, where R 1 is an inside radius of the another dielectric tube and R 2 is an outside radius of the another dielectric tube, such that the relative dielectric constant of the another dielectric tube and the another gas are determined by a cylindrical tube assembly equation wherein the relative dielectric constant of the structural dielectric matches with a result of the elliptical tube assembly equation, and the cylindrical tube assembly equation is:

ɛ

3

=

ɛ

2

⁡

[

R

1

2

⁡

(

ɛ

1

-

ɛ

2

)

+

R

2

2

⁡

(

ɛ

1

+

ɛ

2

)

R

1

2

⁡

(

ɛ

2

-

ɛ

1

)

+

R

2

2

⁡

(

ɛ

1

+

ɛ

2

)

]

.

9. The method as claimed in claim 6 wherein positioning the metal electrodes includes positioning the metal electrodes in direct contact with the dielectric tube.

10. The method as claimed in claim 6 wherein positioning the metal electrodes includes positioning the metal electrodes on the structural dielectric and spaced away from the dielectric tube.

11. A dielectric electrode assembly comprising:

a dielectric tube having a cylindrical cross-section and a relative dielectric constant, ε 2 , the dielectric tube filled with a gas having a relative dielectric constant, ε 1 ;

a structural dielectric having a relative dielectric constant, ε 3 surrounding the dielectric tube;

metal electrodes on opposite sides of the structural dielectric, the metal electrodes having a flat cross-sectional geometry; and

the structural dielectric made from a material selected such that the relative dielectric constants of the structural dielectric, the dielectric tube, and the gas are interrelated and a uniform electric field is generated within the dielectric tube when power is applied to the metal electrodes.

12. The dielectric electrode assembly of claim 11 wherein:

R 1 is an inside radius of the dielectric tube and R 2 is an outside radius of the dielectric tube; and

the material for the structural dielectric is selected such that the relative dielectric constants of the structural dielectric, the dielectric tube, and the gas are related by a cylindrical tube assembly equation of:

ɛ

3

=

ɛ

2

⁡

[

R

1

2

⁡

(

ɛ

1

-

ɛ

2

)

+

R

2

2

⁡

(

ɛ

1

+

ɛ

2

)

R

1

2

⁡

(

ɛ

2

-

ɛ

1

)

+

R

2

2

⁡

(

ɛ

1

+

ɛ

2

)

]

.

13. The dielectric electrode assembly of claim 11 wherein the metal electrodes have an electrode width of at least one dielectric tube diameter past an edge of the dielectric tube and the metal electrodes are on the structural dielectric.

14. The dielectric electrode assembly of claim 11 wherein the metal electrodes are in direct contact with the dielectric tube.

15. The dielectric electrode assembly of claim 11 wherein the metal electrodes are on the structural dielectric and spaced away from the dielectric tube.

16. The dielectric electrode assembly of claim 11 further comprising:

another dielectric tube within the structural dielectric, the another dielectric tube having an elliptical cross-section and a relative dielectric constant, ε 2 , the dielectric tube filled with a second gas having a relative dielectric constant, ε 1 ;

wherein:

an interior surface of the dielectric tube has semi-major axis dimension, A 1 and semi-minor axis dimension, B 1 ;

an exterior surface of the dielectric tube has semi-major axis dimension, A 2 and semi-minor axis dimension, B 2 ;

the relative dielectric constant of the second gas, ε 1 , has a value of 1; and

the material for the structural dielectric and a material of the dielectric tube are selected such that the relative dielectric constant of the dielectric tube, ε 2 , and the relative dielectric constant of the structural dielectric, ε 3 , are related by an elliptical tube assembly equation of:

ɛ

3

=

ɛ

2

⁢

B

2

A

2

⁡

[

A

2

⁢

A

1

2

-

A

1

⁢

B

1

⁢

B

2

+

(

A

1

⁢

B

1

⁢

B

2

-

A

2

⁢

B

1

2

)

⁢

ɛ

2

B

2

⁢

A

1

2

-

A

1

⁢

B

1

⁢

A

2

+

(

A

1

⁢

B

1

⁢

A

2

-

B

2

⁢

B

1

2

)

⁢

ɛ

2

]

.

17. The dielectric electrode assembly of claim 16 wherein the metal electrodes are in direct contact with the another dielectric tube.

18. The dielectric electrode assembly of claim 16 wherein the metal electrodes are on the structural dielectric and spaced away from the another dielectric tube.

19. The dielectric electrode assembly of claim 16 wherein the metal electrodes have rounded edges.

20. The dielectric electrode assembly of claim 16 wherein the metal electrodes are parallel to each other at opposite sides of the structural dielectric.

21. A dielectric electrode assembly comprising:

a dielectric tube having a cylindrical cross-section and a relative dielectric constant, ε 2 , the dielectric tube filled with a gas having a relative dielectric constant, ε 1 ;

a structural dielectric having a relative dielectric constant, ε 3 surrounding the dielectric tube; and

metal electrodes on opposite sides of the structural dielectric, the metal electrodes having a flat cross-sectional geometry;

wherein the relative dielectric constant ε 1 , the relative dielectric constant ε 2 , and the relative dielectric constant ε 3 , are related by an equation:

ɛ

3

=

ɛ

2

⁡

[

R

1

2

⁡

(

ɛ

1

-

ɛ

2

)

+

R

2

2

⁡

(

ɛ

1

+

ɛ

2

)

R

1

2

⁡

(

ɛ

2

-

ɛ

1

)

+

R

2

2

⁡

(

ɛ

1

+

ɛ

2

)

]

;

wherein R 1 is an inside radius of the dielectric tube and R 2 is an outside radius of the dielectric tube.