# Dispersion of Electromagnetic Waves Guided by an Open Tape Helix I

##### Citations

62 citations

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### Cites result from "Dispersion of Electromagnetic Waves..."

...In contrast to previous approaches based on localized resonances, negative refraction in long metallic helix arrays originates from the band-folding effect of propagating helical modes in a periodic helix, as has been shown in previous studies of helical tubes and helical waveguides [143-146]....

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12 citations

##### References

359 citations

### "Dispersion of Electromagnetic Waves..." refers background or methods in this paper

...Hence, the Borgnis potentials [4] for guidedwave solutions, at the radian frequency ω, may be assumed in the form...

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...Since the formulation of the cold-wave problem for the tape helix has become quite standard, we make use of the notation and terminology employed in one of the conventional treatments following Sensiper [1] of the problem as presented in [4] except that we use w, instead of δ, to denote the width of the tape in the axial direction....

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...The explicit expressions for the field components become [4]...

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...in view of Floquet’s theorem [4, 5] where β0 = β0(ω) is the guided wave propagation constant at the radian frequency ω....

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207 citations

### "Dispersion of Electromagnetic Waves..." refers background in this paper

...In fact, the approximate dispersion equations derived by Chodorow and Chu and Watkins have a form identical to that of (30)....

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...Thus, the terms of the series in (30) and those in [2] and [3] decrease rapidly enough with |n| (due to the presence of (sinc)2 factors) to enable the infinite series to be symmetrically truncated to a low order without appreciable error....

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...The rationale behind the approach of Chodorow and Chu for single-wire helix has been outlined by Watkins in his book [3] assuming that (i) the tape current flows only along the winding direction, (ii) it does not vary in phase or amplitude over the width of the tape, and (iii) its phase variation is according to β0z for z corresponding to a point moving along the centerline of the tape....

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...The value of the multiplying factor Rn in (31) is decided by the type of assumption made regarding the tape-current distribution, and irrespective of the particular assumption made, the decay of Rn with respect to n turns out to be no better than |n|−1 except for the case of the one-term approximation to the tape-current distribution made by Chodorow and Chu [2] and Watkins [3]....

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185 citations

95 citations

### "Dispersion of Electromagnetic Waves..." refers methods in this paper

...Since the formulation of the cold-wave problem for the tape helix has become quite standard, we make use of the notation and terminology employed in one of the conventional treatments following Sensiper [1] of the problem as presented in [4] except that we use w, instead of δ, to denote the width of the tape in the axial direction....

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...An indepth study of electromagnetic wave propagation on helical conductors has been performed by Samuel Sensiper way back in 1952 [1]....

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47 citations

### "Dispersion of Electromagnetic Waves..." refers background in this paper

...The rationale behind the approach of Chodorow and Chu for single-wire helix has been outlined by Watkins in his book [3] assuming that (i) the tape current flows only along the winding direction, (ii) it does not vary in phase or amplitude over the width of the tape, and (iii) its phase variation is according to β0z for z corresponding to a point moving along the centerline of the tape....

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...A notable exception to the practice of satisfying the tangential electric field boundary condition only along the centerline of the tape is the variational formulation developed by Chodorow and Chu [2] for cross-wound twin helices wherein the error in satisfying the tangential electric field boundary condition is minimized for an assumed tapecurrent distribution by making the average error equal to zero....

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...Thus, the terms of the series in (30) and those in [2] and [3] decrease rapidly enough with |n| (due to the presence of (sinc)2 factors) to enable the infinite series to be symmetrically truncated to a low order without appreciable error....

[...]

...The value of the multiplying factor Rn in (31) is decided by the type of assumption made regarding the tape-current distribution, and irrespective of the particular assumption made, the decay of Rn with respect to n turns out to be no better than |n|−1 except for the case of the one-term approximation to the tape-current distribution made by Chodorow and Chu [2] and Watkins [3]....

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...In fact, the approximate dispersion equations derived by Chodorow and Chu and Watkins have a form identical to that of (30)....

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##### Related Papers (5)

##### Frequently Asked Questions (12)

###### Q2. What are the future works mentioned in the paper "Dispersion of electromagnetic waves guided by an open tape helix i" ?

Based on the outcome of such a study ( which is currently under progress ), it is proposed to extend the method adopted for the derivation of the tape-helix dispersion equation to a full field analysis of the practically important case of a dielectric-loaded helical slow-wave structure enclosed in a coaxial metal cylindrical shell and supported by azimuthally symmetrically placed dielectric rods. The effect of the dielectric support rods will have to be modeled by a homogeneous dielectric the effective dielectric constant of which can be determined in terms of the geometric arrangement of the support rods and the actual dielectric constant of the rod material.

###### Q3. What is the way to solve the tape helix problem?

The hypothesis that the transverse component of the tape-current density is zero may be incorporated explicitly into the model by assuming that the tape helix is made out of an anisotropic material exhibiting infinite conductivity in the winding direction but zero conductivity in the orthogonal direction.

###### Q4. What is the helix of the tape?

A tape helix of infinite length, constant pitch, constant tape width and infinitesimal thickness surrounded by free space is considered.

###### Q5. What is the effect of the dielectric support rods?

The effect of the dielectric support rods will have to be modeled by a homogeneous dielectric the effective dielectric constant of which can be determined in terms of the geometric arrangement of the support rods and the actual dielectric constant of the rod material.

###### Q6. What is the way to estimate the tape-helix dispersion characteristic?

Since the dispersion curves for N = 2, 3 and 4 are virtually indistinguishable from one another, a truncation order as low as 2 is adequate to deliver an accurate estimate of the tape-helix dispersion characteristic (at least within the validity limits of the assumed model for the parameter values used in the numerical computations).

###### Q7. What is the symmetric dependence of the function FN on i?

The symmetric dependence of the function FN on σ±i, 1 ≤ i ≤ N , implies that if β0a satisfies the dispersion equation (47) for a given k0a so does −β0a for the same k0a.

###### Q8. What is the reason behind the tape-helix approach?

The rationale behind the approach of Chodorow and Chu for single-wire helix has been outlined by Watkins in his book [3] assuming that (i) the tape current flows only along the winding direction, (ii) it does not vary in phase or amplitude over the width of the tape, and (iii) its phase variation is according to β0z for z corresponding to a point moving along the centerline of the tape.

###### Q9. What is the effect of the nth space harmonic on the tape-helix dis?

It is thus seen that the mode constant τ−na of the −nth space-harmonic contribution to the total field becomes imaginary in the nth forbidden region, and that the resultant Poynting vector acquires a small radial component in order to account for the radiation of power from the −nth space harmonic.

###### Q10. What is the dispersion equation for k0a?

Tape-helix dispersion curves for the truncation orders of 0 and 1 are not shown because the iterations for these two cases could not be continued (to convergence) beyond β0a = 4.64 to yield real values for k0a(β0a) in the complement of the forbidden regions.

###### Q11. what is the boundary condition of the nth sheath helix?

In this caseαkq → ∞∑n=−∞ σnδknδqn = σkδkqand the dispersion equation (26) degenerates to∞∏k=−∞ σk = 0that is, σn = 0, n = 0,±1,±2, . . . (28)The relation σn = 0 may be recognized as the dispersion equation for the nth mode of a sheath helix made of the same anisotropically conducting material as the tape helix provided βn, as a whole, is interpreted as the propagation constant of the nth sheath-helix mode.

###### Q12. What is the truncation order of the sheath-helix model?

5. It may be seen from Fig. 5 that the phase speed for the tape-helix model is lower than that for the sheath-helix model for the same value of ω in the complement of the forbidden regions.