• Which Products are you interested in ?

    CST offers a wide range of EM simulation software to address design challenges across the electromagnetic spectrum, from static and low frequency to microwave and RF, for a range of applications, including EDA & electronics, EMC & EMI and charged particle dynamics.

  • CST STUDIO SUITE
  • CST EMC STUDIO
  • CST BOARDCHECK
  • Antenna Magus
  • IdEM
  • FEST3D
  • Optenni Lab
  • Looking for a Training, Workshop or eSeminar ?

    CST STUDIO SUITE® is being demonstrated at trade shows and workshops all over the world. Take a look at the list of conferences and exhibitions CST will be attending and get further information regarding CST workshops, eSeminars and training days.

  • TrainingsRegular training courses are held in CST's offices in Asia, Europe, and North America. Please check our trainings section for detail of trainings in all over the globe. Advance registration is normally required.

  • WorkshopsCST hosts workshops in multiple languages and in countries around the world. Workshops provide an opportunity to learn about specific applications and refresh your skills with experienced CST support staff. Make sure you visit our workshop section.

  • eSeminarsThroughout the year, CST simulation experts present eSeminars on the applications, features and usage of our software. You can also view past eSeminars by searching our archive and filtering for the markets or industries that interest you most.

  • Check our latest Events
  • Why create a MyCST Account ?

    A MyCST account may facilitate your access to many of the offerings on the CST website, for example the registration for eSeminars and the watching of eSeminars recordings, setting email preferences, and there is more functionality to come. It is required to participate in workshops and trainings.

  • Personal PreferencesAllows you to update your email preferences and areas of interest. It helps us to personalize your experience.

  • EventsSearch for events by location, industry and application. Once you are registered, you will be able to manage your registrations and check important details about your events. This section also provides you with a repository for Workshop & Training material.

  • LibraryYou can collect articles you find on the CST website to reference or read later by clicking on the “Add this article” button at the bottom of the article page.

  • Create Your Own Account
  • Need technical Support ?

    Customers can customize their accounts once they have completed the account creation process. This platform acts as vivid interface between CST and our customers.

    We therefore offer access to the latest Service Packs (including an automatic notification that a new Service Pack is available), a steadily growing database of Frequently Asked Questions (FAQs), Application Notes and Training Videos, as well as an individual FTP section for easy exchange of large files with our support team.

  • Do I need an Account?To access the Support Site a valid maintenance contract and a one-time registration is required.

    Please note that your Support login does not work for the MyCST account.

  • Get Support
  • How to request a Trial License ?

    Get your license in only three steps:

    1. Fill in the required fields in the contact form on the right and click "Send Us Your Request".

    2. Lean back and wait until one of our CST Experts contacts you.

    3. Enjoy a our trial license.

  • Student Edition

    Student Edition The CST STUDIO SUITE® Student Edition has been developed with the aim of introducing you to the world of electromagnetic simulation, making Maxwell’s equations easier to understand than ever. With this edition you have, bar some restrictions, access to our powerful visualization engine and some of the most advanced solvers of CST STUDIO SUITE.

    Student Edition

CST – Computer Simulation Technology

Helmholtz Coil


B-field distribution around the Helmholtz coils. The wire coils are located inside the rings of vacuum. Figure 1: B-field distribution around the Helmholtz coils. The wire coils are located inside the rings of vacuum.

The Physics

The Helmholtz coil refers to the arrangement of two conductor loops which generate an almost homogeneous magnetic field in the center of the structure (Fig. 1). With the assumption of an infinitely thin current path, the theoretical solution can be derived as shown e.g. in [1].

Setup of the Helmholtz Coil
Figure 2: Setup of the Helmholtz Coil, with the parameters labeled.

 

Using the Biot-Savart law the magnetic field is determined on the z-axis of the arrangement of Fig.2, as

Bz(z)=
1
2
(
μ0a2I
(a2+(zd)2)(32)
+
μ0a2I
(a2+(z+d)2)(32)
)

 

where µ0 is the permeability of free space.

By using a Taylor expansion to analyze the dependence of the function of the z coordinate the optimum arrangement is found to be 2d=a.

The Model

Two curves are designed and a current is imprinted on them. The boundary conditions should be 'open' with a sufficient distance to the coils. It is possible to activate three symmetry conditions to reduce the mesh requirements – electric in the XZ and YZ planes, and magnetic in the XY plane. If the value for the radius is set (in this example, all given values are in m), the distance of the loops is determined automatically via the parameter list and so the dependencies are correctly considered. By evaluating the resulting fields on the z-axis, the field strengths can be compared to the numerical results. For this purpose the corresponding post-processing templates are used.

CST model setup according to [Henke].
Figure 3: The setup of the Helmholtz Coil in CST Studio Suite®, showing the curves (left) and the 3D dummy objects (right)

 

Parameter Value Description
a 5 mm Coil radius
d a/2 (2.5 m) Distance of coil from midpoint
l 1 A Current around each coil

 

For the evaluation of the field values along the curve one has to ensure that adequate interpolation points are available. It is also helpful to have a dense mesh surrounding the current paths. To allow the mesh to be redefined within the mesh limitations of the CST Studio Suite Student Edition, dummy structures are introduced surrounding the current paths and along the z-axis (Fig. 3). These structures have the same material properties as the background material (vacuum) and ensure a finer mesh generation in this region. These are constructed with around the curves, with a radius of a/10 around each curve.

 

Model Construction Watch Video

Download Model File (Student Edition) Download Model File

Discussion of Results


Template Based Post Processing dialog
Figure 4: The Template Based Post Processing dialog, showing the Evaluate Field on Curve option.

 

Template Based Post Processing (Fig. 4) is used to calculate the BZ field along the line. Set up the template as shown in Fig. 5, and click "Evaluate" in the main Template Based Post Processing window to calculate the field distribution along the curve.

Helmholtz-Coil-PostProcessing-Evaluate-Field-on-Curve
Figure 5: The Evaluate Field on Curve template

 

This can be compared directly with the theoretical results. Equation 1 can be represented in a calculable format as:

1/2*mue0*a^2*I*(1/(a^2+(A-d)^2)^(3/2)+1/(a^2+(A+d)^2)^(3/2)), where A is the Z coordinate.

By pasting this into the “Mix Template Results” post processing template (Fig. 6), which is found under "General 1D" in the Template Based Post Processing window, the numerical Bz along the z-axis can be calculated.


Helmholtz-Coil-PostProcessing-Mix-Field
Figure 6: The Mix Template Results dialog, with Equation 1 pasted in. Helmholtz-Coil-Result-Curve
Figure 7: B-Field along z-axis – a comparison of analytical and numerical results

 

Comparing the theoretical and numerical results in Fig. 7 shows that a very good agreement is found. To achieve such a good agreement, the described usage of dummy structures is essential.

Questions


Helmholtz-Coil-Setup-Coil
Figure 8: 3D coil definition

 

Q1: The coil function (Fig. 8) can be used to define 3D coils, by sweeping a “profile” curve (representing the cross-section of the coil) along a path curve. Define two 3D coils in place of the dummy structures – how do the results change?

Q2: What is the effect of changing the symmetry between the loops to electric?

References

  • [1] H. Henke, Elektromagnetische Felder: Theorie und Anwendung, 3. erweiterte Auflage, Springer-Lehrbuch, pp. 177-179
contact support

Your session has expired. Redirecting you to the login page...

We use cookie to operate this website, improve its usability, personalize your experience, and track visits. By continuing to use this site, you are consenting to use of cookies. You have the possibility to manage the parameters and choose whether to accept certain cookies while on the site. For more information, please read our updated privacy policy


Cookie Management

When you browse our website, cookies are enabled by default and data may be read or stored locally on your device. You can set your preferences below:


Functional cookies

These cookies enable additional functionality like saving preferences, allowing social interactions and analyzing usage for site optimization.


Advertising cookies

These cookies enable us and third parties to serve ads that are relevant to your interests.