When such an attack is precipitated by an infection bacteria living or nonliving purchase 100 mg vibramycin visa, it is much more likely to treatment for dogs with gingivitis order vibramycin 100 mg with amex be viral than bacterial antimicrobial eye drops vibramycin 100 mg sale. The role of bacterial infection is often overestimated; however antibiotics should be reserved for relatively rare cases in which there is strong evidence of a bacterial infection antibiotics for dogs for sale cheap vibramycin 100mg on line, such as pneumonia or bacterial sinusitis. Potential harms of unnecessary antibiotic treatment include medication costs, side-effects (including a risk of allergy), and emergence of bacterial resistance. Given that scores between the 5th and 6th rated recommendations were close, 6 recommendations were adopted. Diagnosis and management of stable chronic obstructive pulmonary disease: a clinical practice guideline update from the American College of Physicians, American College of Chest Physicians, American Thoracic Society, and European Respiratory Society. United States of America Department of Veterans Affairs and the Department of Defense. Critical issues in the evaluation and management of adult patients presenting to the emergency department with suspected pulmonary embolism. Time trends in pulmonary embolism in the United States: evidence of overdiagnosis. Comparing patients? expectations with data from a systematic review of the literature. Principles of appropriate antibiotic use for treatment of acute bronchitis in adults. Canadian Thoracic Society 2012 guideline update: diagnosis and management of asthma in preschoolers, children and adults [Internet]. Uniform defnition of asthma severity, control, and exacerbations: document presented for the World Health Organization Consultation on Severe Asthma. Joint task force report: supplemental recommendations for the management and follow-up of asthma exacerbations. If bone mineral densities are stable and/or individuals are at low risk of fracture, then less frequent monitoring up to an interval of 5-10 years can be considered. The 2008 Cochrane Reviews for three bisphosphonates (Alendronate, Etidronate, Risedronate) found no statistically signifcant reductions for primary prevention of fracture in postmenopausal women. Given the lack of proven effcacy, widespread use of bisphosphonates in patients at low risk of fracture is not currently recommended. The diagnosis of peripheral and axial infammatory arthritis can usually be made on the basis of an appropriate history, physical exam and basic investigations. A methodology subcommittee discussed the items in light of their relevance to rheumatology, potential impact on patients and the member survey results. Guidelines for clinical use of the antinuclear antibody test and tests for specifc autoantibodies to nuclear antigens. Evidence-based guidelines for the use of immunologic tests: Antinuclear antibody testing. Guidelines for the laboratory use of autoantibody tests in the diagnosis and monitoring of autoimmune rheumatic diseases. Evidence-based recommendations for the management of ankylosing spondylitis: Systematic literature search of the 3E initiative in rheumatology involving a broad panel of experts and practising rheumatologists. Executive summary of the 2013 international society for clinical densitometry position development conference on bone densitometry. Alendronate for the primary and secondary prevention of osteoporotic fractures in postmenopausal women. Etidronate for the primary and secondary prevention of osteoporotic fractures in postmenopausal women. Risedronate for the primary and secondary prevention of osteoporotic fractures in postmenopausal women. Do tc-99m-diphosphonate bone scans have any place in the investigation of polyarthralgia? The diagnostic value of scintigraphy in assessing sacroiliitis in ankylosing spondylitis: A systematic literature research. Isotope bone scans: An assessment of their diagnostic use in polyarticular pain of uncertain origin. This includes an amazing lineup of topics and speakers for the Annual Scientifc Meeting, a website full of information, programs to attract more medical students into rheumatology, awards to recognize its members, guidelines development, research funding opportunities and excellent working partnerships with other organizations. For over half a century back pain has been the most common reason for spinal fusion. Yet there is no unequivocal evidence that fusion is superior to comprehensive conservative treatment for treating back pain without focal structural pathology and concordant mechanical or neurological symptoms. It is often impossible to locate the precise source of the pain; in many cases the symptoms are multifactorial and can encompass elements such as centralized pain that exist outside the spine. The extreme heterogeneity of the low back pain population leads to unpredictable surgical results and consistently poor outcomes in those with pain from multilevel spine degeneration. Don?t routinely image patients with low back pain regardless of the duration of symptoms 2 unless. Unless the image has a direct bearing on the treatment decision it is not required. Spinal abnormalities? in asymptomatic individuals are common and increase with age. For the majority of low back complaints obtaining spinal imaging does not improve patient care but can lead to inappropriate interventions and does have a detrimental impact on patient outcomes. Red fags include cauda equina syndrome; severe or progressive neurologic defcits; suspected cancer; suspected infection: suspected fracture and suspected epidural abscess or hematoma. Steroids are potent anti-infammatory agents, but axial low back pain is not primarily an infammatory condition and any infammation that does exist generally cannot be accessed via the spinal canal. Although serious adverse events are rare, catastrophic events can occur and any symptom relief from the injection typically lasts only for a matter of weeks. In light of the resulting decrease in the indications for surgical intervention, the bias against bracing should be reevaluated. Don?t order peri-operative antibiotics beyond a 24-hour post-operative period for non 5 complicated instrumented cases in patients who are not at high risk for infection or wound contamination. Administration of a single pre-operative dose for spine cases without instrumentation is adequate. Although a deep surgical site infection associated with spinal implants can be a devastating adverse event, the prolonged use of peri-operative antibiotics has not been shown to reduce the incidence. Their extended use in routine low risk cases has no proven evidence of beneft but increases the chance of creating resistant bacterial strains. Don?t use an opioid analgesic medication as frst-line treatment for acute, uncomplicated, 6 mechanical, back-dominant pain. Over 90% of acute low back pain is a mechanical problem that is often self-limiting and can be controlled with physical treatment and non-narcotic medication. The most common entry point to prescription opioid addiction is through opioids prescribed for back pain. Adequate pain control using opioids is frequently not achieved and patients face the added risks of physical dependence and withdrawal hyperalgesia, which can lead to continued use. Don?t treat post-operative back pain with opioid analgesic medication unless it is 7 functionally directed and strictly time limited. Using post-operative opioid analgesics creates problems with constipation, nausea and dizziness while interfering with early mobilization and, in some patients, promoting long term use. It should be used only in a strictly limited manner and with well-defned parameters. Alternate pain management regimens offer improved pain control, enhanced rehabilitation and fewer complications. Don?t use opioid analgesic medication in the ongoing treatment of chronic, non-malignant 8 back pain. There is no clear evidence for the benefts of long-term opioid medication on pain, function or quality of life. There is a clear correlation with a range of adverse effects including falls, fractures, testosterone suppression, hyperalgesia and depression. Long-term use either before or following spine surgery is associated with increased medical costs and a reduced rate of return to work. The amended list was recirculated, revised and sent to the membership for a third time. Recommendations 6-8: the Canadian Spine Society conducted a survey of its membership, which includes both academic and private neurosurgical and orthopaedic spine surgeons, on the use of opioids from back pain. The members were asked to specify both the nature of the back problem and the role for opioid medication. Surgery for low back pain: a review of the evidence for an American Pain Society Clinical Practice Guideline.
Standard protocol Certain lines may require further optimisation of plating density to infection low body temperature order vibramycin paypal 1 virus ny 100 mg vibramycin amex. It is advantageous to antibiotics for dogs amoxicillin order vibramycin without a prescription use clones that go through the targeting process but that have not been edited as control cell lines bacteria kingdoms buy vibramycin 100mg. Representative images of cells at different stages of neural Puromycin (depending on the strategy) differentiation. Cell and 96-well plates for single clone picking death might become apparent once cultures become confluent. Falcon tubes (C) Immunostaining for Sox1 and the post-mitotic marker Tuj1 on days 4 and 6 Centrifuge of differentiation. Just before counting cells, combine mix A and B to obtain negative; day 3, predominantly Sox2 positive (cells should be 400 l transfection reaction. Evenly disperse cells by sliding plate vertically and horizontally across a flat surface. A 6-well plate format should be used with a cell concentration 5 Each transfection will require 300,000 cells per well (round dish of 1-2? Under an inverted or dissection microscope in a flow cabinet, chances of cell lines becoming compromised. Note: differentiation can be initiated at this point Pasteur pipettes by changing medium to N2B27. Note: Blast Do not leave the cells in the transfection media for more than media (Origio) can be used as an alternative, but N2B27 is? Incubate for 1 or 2 more days, depending on when the embryos were transferred to N2B27. On day 3 of culture, pre-equilibrate an organ culture dish containing N2B27+20% anti-mouse serum and three dishes containing 400 l N2B27 in the incubator. Transfer embryos still contained within the zona pellucida to independent experiments. Place embryos in a pre-equilibrated dish containing Three main tests are carried out on batches of N2B27 to determine N2B27+20% anti-mouse serum. Rinse three times in pre-equilibrated N2B27 (or M2, if Colony-formation assay preferred) by transferring embryos through drops. Next day, change medium to fresh 2i/ immunostaining for Nanog can also be performed. Repeat passaging procedure, progressively expanding batches result in relatively uniform Nanog expression across the line to 48-well, 24-well, etc. Troubleshooting tips Problem Cause Solution Colonies show poor Residual dissociation media present. After spinning cell suspension with Accutase and wash buffer, make sure attachment and float no residue remains. Cells were overgrown/underfed; mistreatment It is recommended to thaw a new vial of cells. Verify under the sizes microscope after pipetting to dissociate and before transferring to tube with 5? Avoid circular motions of the plate and open/close incubators gently until cells have settled. Although morphology can be recovered after plating at single cell density, colonies the damage to cells is normally irreversible. The main effect of overgrowing cells is that they can no longer differentiate efficiently. Good batches of N2B27 show little cell death until cells reach Supplementary information confluence. Parameters influencing comprehensive set of step-by-step protocols, including all media derivation of embryonic stem cells from murine embryos. Feedback on these inner-cell-mass cells to self-renew as embryonic stem cells is acquired following protocols and recommendations for further improvement are epiblast specification. The origin and efficient derivation of We thank all past and present members of the Smith and Nichols lab for embryonic stem cells in the mouse. Gene targeting in mice: functional analysis of the acknowledge Balazs Vargaand for testing N2B27 formulations and Sally Lees mammalian genome for the twenty-first century. Nanog safeguards Competing interests pluripotency and mediates germline development. Science fine tunesthe dynamics of acell state transition involving Lin28, let-7 and de novo 344, 1156-1160. Reconstitution of the mouse germ cell specification pathway in culture by Miller, A. Cold transcription factor functions empower formative transition from naive Spring Harbor Perspect. In Teratocarcinomas and Germline potential of parthenogenetic haploid mouse embryonic stem cells. Formative pluripotency: the executive phase in a developmental exhibit properties consistent with ageneric pluripotent ground state. Inhibition of pluripotential embryonic stem cell differentiation by purified Mansfield, W. Inhibition of glycogen synthase kinase-3 alleviates Tcf3 embryonic stem cells into neuroectodermal precursors in adherent monoculture. This Stem Cell Research Laboratory, Department of Biotechnology, Delhi Technological University, novel technology enables derivation of patient specific cells, which possess a potential cure for many diseases. Delhi-110042, India 3 During the last decade, significant progresses have been Dr. Nevertheless, it is important to resolve and define the mechanism underlying the pluripotent stem cells. Vimal Kishor Singh: Founder & O/I Stem Cell Research Laboratory, Department of Biotechnology, Delhi Technological University, Shahbad Daulatpur, Bawana Road, Delhi-110042 vim kissor@yahoo. All these personalized medicine, curing a broad range of studies were valuable and helpful to reprogram the diseases. In 1938, Spemann first proposed nuclear transfer Different sources have different limitations in their but experiment was unsuccessful  then, in 1952, own processing and use. However, they were not able to reproduce efficiencies have different requirements of lab setup the process with other specialized cells. Retroviral delivery systems Gurdon studied the similar experiment on tadpole, but were the first used for introduction of transgenes into unfortunately did not succeed when used similar the host cell, but they lack the ability to introduce at technique on other species . This may cause insertional was achieved with demonstration of cloning mutagenesis or teratoma formation. Lentiviral technique for Dolly sheep which was developed with systems overcome the tumour formation and hence, Mechanism of Induction: Induced Pluripotent Stem Cells 45 are used in reprogramming. Dox lentiviral system and single poly revolutionized the field of clinical therapy. Direct delivery methods have been in modelling of many diseases, drug discovery and defined to reduce the risk of genetic modification. But, there have how reprogramming factors are involved in been studies where researchers have not used one or pluripotency. Small molecules are mostly regulate an adult cell to repress the genes responsible involved in epigenetic regulation via inhibiting for differentiation and activate the genes responsible nucleosome remodelling complexes. Reprogramming suitable somatic cell source is required which is easily mechanism involves expression of genes responsible accessible, available and convenient in processing. Various epigenetically and more importantly avoid any risk of markers have been used for the selection and tumours. Another important aspect is the 46 Vimal Kishor Singh, Neeraj Kumar, Manisha Kalsan et al. Since exact other cell sources, for example, cord blood, peripheral mechanism and the role of transcription factor is blood, urine, keratinocytes etc, delivery methods other unclear, some valuable insights into molecular than viral methods, non viral methods and direct mechanisms are required, by which, cellular fate and delivery methods have been developed. Induction of reprogramming factors suppresses the genes responsible for cell differentiation and activates pluripotency maintaining genes. Alternatives of the transcription Overexpression of embryonic transcription factors factors, other reprogramming cocktail combinations deletes the somatic cell properties and restores the and small molecules have been found to reprogram pluripotency [19, 20]. Subsequent study reported production of associated with certain issues such as lower successful animal clones using different somatic cell reprogramming efficiency and teratoma formation.
Label free hepatitis B detection based on serum derivative surface-enhanced Raman spectroscopy combined with multivariate analysis treatment for dogs back legs vibramycin 100 mg without prescription. Lab-on-a-chip-surface-enhanced Raman scattering combined with the standard addition method: Toward the quantification of nitroxoline in spiked human urine samples antimicrobial breakpoints discount vibramycin. Quantitative detection of acyclovir by surface-enhanced Raman spectroscopy using a portable Raman spectrometer coupled with multivariate data analysis on antibiotics for sinus infection generic 100mg vibramycin free shipping. Global antimicrobial vs antibiotics cheap vibramycin 100 mg visa, regional, and national cancer incidence, mortality, years of life lost, years lived with disability, and disability-adjusted life-years for 32 cancer groups, 1990 to 2015 a systematic analysis for the global burden of disease study. A simple electrochemical immunosensor platform for detection of apolipoprotein A1 (Apo-A1) as a bladder cancer biomarker in urine. Measurement of the IgM and IgG autoantibody immune responses in human serum has high predictive value for the presence of colorectal cancer. Fluorescent immunosensor based on CuS nanoparticles for sensitive detection of cancer biomarker. Highly sensitive immunoassay of lung cancer marker carcinoembryonic antigen using surface-enhanced Raman scattering of hallow gold nanospheres. Multiplexed sers detection of soluble cancer protein biomarkers with gold-silver alloy nanoboxes and nanoyeast single-chain variable fragments. Fabrication of plasmon length-based surface-enhanced Raman scattering for multiplex detection on micro? Antibody-free discrimination of protein biomarkers in human serum based on surface-enhanced Raman spectroscopy. In vivo tumor targeting and spectroscopic detection with surface-enhanced Raman nanoparticle tags. Int/sustainable-development/housing/ health-risks/waterborne-disease/en/ (accessed on 29 December 2018). Com/campylobacter-on-the-rise in-germany-every-second-chicken-in-germany-is-contaminated/ (accessed on 12 January 2019). Rapid, accurate, and comparative differentiation of clinically and industrially relevant microorganisms via multiple vibrational spectroscopic fingerprinting. Diagnosis of bacterial pathogens in the urine of urinary-tract-infection patients using surface-enhanced Raman spectroscopy. Surface-enhanced Raman spectroscopy of Chlamydia trachomatis and Neisseria gonorrhoeae for diagnostics, and extra-cellular metabolomics and biochemical monitoring. Surface-enhanced Raman spectroscopy for bacterial discrimination utilizing a scanning electron microscope with a Raman spectroscopy interface. Rapid bacterial antibiotic susceptibility test based on simple surface-enhanced Raman spectroscopic biomarkers. Tracking heavy water (D O) incorporation for identifying and sorting2 active microbial cells. Reverse and multiple stable isotope probing to study bacterial metabolism and interactions at the single cell level. Detection of multiple pathogens in serum using silica-encapsulated nanotags in a surface-enhanced Raman scattering-based immunoassay. A point-of-care diagnostic for differentiating Ebola from endemic febrile diseases. Analytical challenges in breath analysis and its application to exposure monitoring. Breath analysis based on surface-enhanced Raman scattering sensors distinguishes early and advanced gastric cancer patients from healthy persons. Ultrasensitive surface-enhanced Raman scattering sensor of gaseous aldehydes as biomarkers of lung cancer on dendritic Ag nanocrystals. Volatile organic compound signature from co-culture of lung epithelial cell line with Pseudomonas aeruginosa. Surface-enhanced Raman spectroscopy for the detection of a metabolic product in the headspace above live bacterial cultures. Quantitative detection of codeine in human plasma using surface-enhanced Raman scattering via adaptation of the isotopic labelling principle. High dilution surface-enhanced Raman spectroscopy for rapid determination of nicotine in e-liquids for electronic cigarettes. Clinical applications of infrared and Raman spectroscopy: state of play and future challenges. Towards a detailed understanding of bacterial metabolism?Spectroscopic characterization of Staphylococcus epidermidis. Development of deep subsurface Raman spectroscopy for medical diagnosis and disease monitoring. Recent advances in the development of Raman spectroscopy for deep non-invasive medical diagnosis. In vivo and in situ spectroscopic imaging by a handheld stimulated Raman scattering microscope. Coherent anti-Stokes Raman scattering microscopy: Chemical imaging for biology and medicine. Combining deep learning and coherent anti-Stokes Raman scattering imaging for automated differential diagnosis of lung cancer. C cell hyperplasia is defned as gland proper and, rarely, can serve as the origin of an consisting of more than 40 C cells/cm2 and the pres intrathyroidal cyst . Parathyroid glands, thymic ence of at least three low-power microscopic felds tissue, small collections of cartilage, and glands lined containing more than 50 C cells . The small by ciliated cells may be seen in normal thyroids, pre solid cell nests of ovoid to spindled epidermoid cells sumably related to defective development of the bran in thyroid are also considered to be of ultimobran chial pouches [31?33]. Typically, the nests have about the Because of the intimate relationship that exists in same distribution in the thyroid lobes as the C cells the embryo between the immature thyroid tissue and [16,17]. The term mixed follicles?  applies to fol the adjacent developing skeletal muscle, strips of stri licles which are lined by follicular cells and epider ated muscle are occasionally included within the thy moid cells (and sometimes C cells) and contain both roid [34?36]. The ultimobranchial Tyroid tissue can be found in close proxim structures probably also give rise to a small propor ity or within the perithyroidal skeletal muscle. Groups of thyroid follicles in lateral cervical lymph The cytoplasm is flled with enlarged mitochondria. A few experienced pa autoimmune thyroiditis, thyroids afected by radia thologists state normal thyroid follicles rarely occur tion, follicular-derived neoplasms, and some adeno in cervical lymph nodes . Also present in the interstitial tissue are antigen-pre senting dendritic cells; these are sparse in the normal gland but are increased in autoimmune thyroid dis 10. Goiter is a difuse or nodular enlargement of the gland usually resulting from a benign process or a 10. When there is a defciency of circulating thyroid hormone because The thyroglossal tract extends in the midline from of inborn errors of metabolism, iodine defciency, or the foramen cecum at the base of the tongue to the goitrogenic agents, and if the hypothalamic-pituitary isthmus of the normal gland . Tyroid tissue may persist at the base of the tongue Worldwide, the most common cause for a defcient and in some patients may be the only thyroid pres output of thyroid hormone is an inadequate amount ent [25,26]. The thyroglossal duct is typically lined of iodine in the diet, leading to iodine-defciency goi by ciliated pseudostratifed epithelium. Other causes of hyper traumatized or infected, the epithelium may undergo plasia include inborn errors of thyroid metabolism alteration to transitional or squamous type, or maybe (dyshormonogenetic goiter) [48,49], dietary goitro totally be replaced by fbrous tissue. If fuid accumulates in part of the thyroglossal ter include one or more of the following: (1) hyper duct, a thyroglossal cyst may develop [3,27,28]. The of thyroglossal duct are included within the thyroid hyperplasia may compensate for thyroid hormonal 10 Tyroid Pathology 111 defciency, but in some cases, even severe hyperplasia does not lead to sufcient hormonal output to avoid development of hypothyroidism. If the defciency of thyroid hormone occurs at birth or early in life, cretinism or juvenile myxedema may result, even though the gland is enlarged and hy perplastic; this is especially likely when an inborn er ror of thyroidal metabolism is present [57,58]. The follicular cells are enlarged and columnar in shape with nuclear enlargement, hyper chromasia, and even pleomorphism. The recognition of the benign na mal iodide concentration, growth-promoting thyroid ture of this process is possible because of its difuse antibodies, and poorly understood intrathyroidal fac nature , unlike carcinoma, in which the tumors tors . If one nodule is much larger called involution, with the hyperplastic follicles reac or more prominent than the others (dominant nod cumulating colloid. The epithelium becomes low cu ule), distinguishing it from a true neoplasm (such as boidal or fattened and resembles that of the normal adenoma) may not be possible [37,63]. The gland is difusely enlarged, sof, and has a ies have shown that about 70% of dominant nodules glistening cut surface because of the excess of stored in nodular goiter are indeed clonal proliferations colloid. The formation of cysts, hemorrhage, fbrosis, loid, there are foci in the gland where hyperplasia is and calcifcation further complicates the assessment still evident (Fig.
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Redness around the surgery site
Lightheadedness when standing
Difficulty lifting up the foot and toes and making toe-out movements
What other symptoms do you have?
Hematoma (blood accumulating under the skin)
Bone graft material may be placed between the vertebrae.
Thinning of the bones (osteoporosis)
In principle antibiotics vs antibodies order vibramycin 100 mg without prescription, it is unnecessary for the power supply to antibiotic resistance and public health purchase 100 mg vibramycin otc support g displacement currents because energy is not absorbed by reactances infection generic 100mg vibramycin fast delivery. The strategy is to xone antibiotic discount vibramycin 100 mg otc add circuit elements than can support the reactive current, leaving the generator to supply power only to the 385 Resonant Cavities and Waveguides resistive load. This is accomplished in the acceleration gap by adding a shunt inductance with 2 value L 1/ oC, where o is the generator frequency. The improvement of the Wideroe linac g by the addition of resonant cavities (Section 14. Matching can also be accomplished by adjusting the length of the transmission line connecting the generator to the loop. At certain values of line length, the reactances of the transmission line act in concert with the reactances of the loop to support displacement current internally. The procedure for finding the correct length consists of adjusting parameters in Eq. The search for a match is aided by use of the Smith chart; the procedure is reviewed in most texts on microwaves. Electromagnetic waves are reflected at the axial boundaries, giving rise to the standing-wave patterns that constitute resonant modes. We shall remove the boundaries in this section and study electromagnetic oscillations that travel in the axial direction. A structure that contains a propagating electromagnetic wave is called a waveguide. Consideration is limited to metal structures with uniform cross section and infinite extent in the z direction. In particular, we will concentrate on the cylindrical waveguide, which is simply a hollow tube. Waveguides are often used in accelerators to couple power from a microwave source to resonant cavities. Furthermore, it is possible to transport particle beams in a waveguide in synchronism with the wave phase velocity so that they continually gain energy. Waveguides used for direct particle acceleration must support slow waves with phase velocity equal to or less than the speed of light. Slow-wave structures have complex boundaries that vary periodically in the axial direction; the treatment of slow waves is deferred to Section 12. Single-frequency waves in a guide have fields of the formexp[j(t kz)] or exp[j(t kz)]. This difference influences the nature of propagating waves in the following ways: 1. This does not violate the principles of relativity since information can be carried only by modulation of wave amplitude or frequency. The propagation velocity of frequency modulations is the group velocity, which is always less than the speed of light in a waveguide. The properties of waveguides are easily demonstrated by a lumped circuit element analogy. We can generate a circuit model for a waveguide by starting from the transmission line model introduced in Section 9. At frequencies low compared to 1/(R R), the field pattern is the familiar one with radial o i electric fields and azimuthal magnetic fields. Displacement current flows radially; longitudinal voltage differences result from inductive fields. The field pattern may be modified when the radius of the center conductor is reduced and the frequency is increased. Consider the limit where the wavelength of the electromagnetic disturbance, 2 /k, is comparable to or less than the outer radius of the line. In this case, voltage varies along the high-inductance center conductor on a length scale Ro. Furthermore, a portion of the longitudinal current flow in the transmission line is carried by displacement current. An equivalent circuit model for the coaxial transmission line at high frequency is shown in Figure 387 Resonant Cavities and Waveguides 12. The flow of real current through inductor L2 is supplemented by axial displacement current through the series combination of C1 and L1. The inductance L1 is included because displacement currents generate magnetic fields. As the diameter of the center conductor is reduced, increasing L2, a greater fraction of the axial current is carried by displacement current. We can use the impedance formalism to find the appropriate wave equations for the circuit of Figure 12. Assume that there is a wave movinginthe+zdirectionandtakevariationsofvoltageandcurrentas 388 Resonant Cavities and Waveguides V V exp[j(t kz)] and I I exp[j(t kz)]. The quantity C2 equals c2 z,wherec2 is the shunt capacitance per unit length in farads per meter. The series capacitance is inversely proportional to length, so that C c z, where c1 is the series capacitance of a unit length. The voltage drop across an element is the impedance of the element multiplied by the current or V I (j z/ c1 j l1 z), or V/ z (j/ c1 j l1) I (12. It determines the phase velocity of waves in the guide as a function of frequency: 2 2 /k c1/c2 c / 1 c/. Low-frequency waves are reflected near the input of the waveguide; the waveguide appears to be a short circuit. The leading zero indicates that there is azimuthal symmetry; the 1 indicates that the mode has the simplest possible radial variation of fields. There are an infinite number of higher-order modes that can occur in a cylindrical transmission line. We will now calculate properties of azimuthally symmetric modes in a cylindrical waveguide by direct solution of the field equations. Again, we seek propagating disturbances of the form E(r,,z,t) E(r,)exp[j(t kz)], (12. The process is complicated by the boundary conditions that must be satisfied at the wall radius, Ro: 390 Resonant Cavities and Waveguides E (Ro) 0, (12. Solutions are divided into two categories: waves that have Ez = 0 and waves that have Bz = 0. Setting Br = 0 at the wall implies the simple, decoupled 391 Resonant Cavities and Waveguides boundary condition Bz(Ro)/ r 0. The only component of electric field parallel to the wall is Ez so that the boundary condition is Ez(Ro) 0. The longitudinal contribution to the Laplacian follows from the assumed form of the propagating wave solution. First, the wavenumber of low-frequency waves is imaginary so there is no propagation. The free-space wavelength is about o o equal to the waveguide diameter; waves with longer wavelengths are shorted out by the metal waveguide walls. It is easy to show that slow waves cannot propagate in waveguides with simple boundaries. Consider, for instance, waves with electric field of the form exp[j(t kz)] with /k < c in a uniform cylindrical pipe of radius Ro. Because the wave velocity is assumed less than the speed of light, we can make a transformation to a frame moving at speed uz = /k. This is not consistent with the fact that the wave is surrounded by a metal pipe at constant potential. The properties of slow 393 Resonant Cavities and Waveguides waves can be derived by a formal mathematical treatment of wave solutions in a periodic structure. In this section, we shall take a more physical approach, examining some special cases to understand how periodic structures support the boundary conditions consistent with slow waves. To begin, we consider the effects of the addition of periodic structures to the transmission line of Figure 12. The magnetic fields are almost identical to those of the standard transmission line except for field exclusion from the irises; this effect is small if the irises are thin. In contrast, radial electric fields cannot penetrate into the region between irises. The electric fields are restricted to the region between the inner conductor and inner radius of the irises. The result is that the inductance per unit length is almost unchanged, but C is significantly increased.